Logic II
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Problem 1
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Institute of Mathematics
University of the Philippines-Diliman
[email protected]
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Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
2011 Math 1
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Inductive vs Deductive
Reasoning
Sample Logic
Problems
Julius Magalona Basilla
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Argument
Common forms of
Deductive Reasoning
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Math 1
General Mathematics
Lecture 6
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Developing a sound argument
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Inductive vs Deductive Reasoning
Logic II
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Observed Patterns
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Conclusions
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Sample Logic
Problems
Inductive Reasoning
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Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
Conclusions
Deductive Reasoning
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Accepted Premises
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Problem 1
Hypothetical Syllogisms
Logic II
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J.M.Basilla
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1. If P then Q.
2. If Q then R.
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Given three statements, P , Q and R.
Known/accepted facts:
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Conclusion: If P then R.
Sample Logic
Problems
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Given 1: If you live in San Fernando then you live in
Pampanga.
Given 2: If you live in Pampanga then you speak
kapangpangan.
Conclusion: If you live in San Fernando then you
speak kapangpangan.
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Problem 1
Example:
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
Hypothetical Syllogisms
Logic II
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J.M.Basilla
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1. If P then Q.
2. If Q then R.
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Given three statements, P , Q and R.
Known/accepted facts:
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Conclusion: If P then R.
Sample Logic
Problems
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Problem 1
Example:
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Problem 3
More Logic Problem
Last Semester’s
Quiz
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Given 1: All good chess players wears glasses.
Given 2: All who wes glasses are nerds..
Conclusion: All good chess players are nerds.
Problem 2
Affirming the antecedent
Logic II
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1. If P then Q.
2. P .
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Given two statements, P and Q.
Known/accepted facts:
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Conclusion: Q.
Sample Logic
Problems
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Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
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Given 1: If I studied for six hours, I will pass the
exams.
Given 2: I studied for six hours.
Conclusion: I will pass the exams.
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Problem 1
Example:
Affirming the antecedent
Logic II
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1. If P then Q.
2. P .
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Given two statements, P and Q.
Known/accepted facts:
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Conclusion: Q.
Sample Logic
Problems
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Problem 1
Example:
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Problem 3
More Logic Problem
Last Semester’s
Quiz
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Given 1: All men are mortal.
Given 2: Socrates is a man.
Conclusion: Socrates is a mortal.
Problem 2
Denying the consequent
Logic II
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1. If P then Q.
2. ∼ Q.
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Given two statements, P and Q.
Known/accepted facts:
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Conclusion: ∼ P .
Sample Logic
Problems
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Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
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Given 1: If it rains the ground will be wet.
Given 2: The ground is not wet.
Conclusion: It did not rain.
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Problem 1
Example:
Denying the consequent
Logic II
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1. If P then Q.
2. ∼ Q.
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Given two statements, P and Q.
Known/accepted facts:
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Conclusion: ∼ P .
Sample Logic
Problems
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Problem 1
Example:
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Problem 3
More Logic Problem
Last Semester’s
Quiz
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Given 1: All US presidents are white.
Given 2: Obama is black.
Conclusion: Obama is not a US president.
Problem 2
Misleading Labels 1
Logic II
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Inductive vs Deductive
Reasoning
Sample Logic
Problems
Problem 1
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Argument
Common forms of
Deductive Reasoning
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gold or silver
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bronze
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gold
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Three chests contain coins. One is labelled
”gold,” a second ”bronze,” a third ”gold or silver.”
One chest contains gold coins only, another
silver coins only, and the third bronze coins only,
but all the chests are incorrectly labelled. Which
chest contains which coins?
Problem 2
Problem 3
More Logic Problem
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C
correct label
silver
gold
bronze
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B
mislabel
gold
bronze
gold or silver
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chest
chest 1
chest 2
chest 3
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Last Semester’s
Quiz
Misleading Labels 2
Logic II
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Problem 1
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Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
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Inductive vs Deductive
Reasoning
Sample Logic
Problems
Hence, the chest do not contain gold coins.
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Argument
Common forms of
Deductive Reasoning
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If the chest contains some gold coins, the label
becomes a contradiction.
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J.M.Basilla
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A chest which might contain some gold coins or
might not is labelled: THIS CHEST DOES NOT
CONTAIN GOLD COINS. It is known that if it
contains gold coins, the label will be true.
Otherwise, if it does not contain gold coin the
label will be false.
Misleading Labels 3
Logic II
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Problem 1
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Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
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Inductive vs Deductive
Reasoning
Sample Logic
Problems
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This chest
contains
the bronze
coins.
Argument
Common forms of
Deductive Reasoning
C
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B
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The gold
coins are in
chest C
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This chest
does
not
contain the
silver coins
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Each of the three chests is labelled with a
statement. One of the chests contains gold
coins, one contains silver coins, and one
contains bronze coins. The statement on the
chest containing gold coins is true, but the
statement on the other two chests are false. The
label were as follows
Misleading Labels 3
B
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Logic II
J.M.Basilla
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Problem 1
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Since, the label on B is false, then chest A contains
the gold coins.
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Chest C cannot contain the gold. And the label on
chest C is false. Therefore, chest B contains bronze
JB
Inductive vs Deductive
Reasoning
Sample Logic
Problems
If B contains the gold coins. The label should have
been the golds are in chest B. Therefore, B contains
silver or bronze and the label must be false.
Chest C contains silver.
Argument
Common forms of
Deductive Reasoning
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A
This chest
contains
the bronze
coins.
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The gold
coins are in
chest C
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This chest
does
not
contain the
silver coins
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
Misleading Labels 4
Logic II
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Problem 1
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Inductive vs Deductive
Reasoning
Sample Logic
Problems
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Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
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Argument
Common forms of
Deductive Reasoning
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J.M.Basilla
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Three chests contain either coins of gold or
worthless lumps of clay. The following are
known.
1. If chest C contains clay then chest B
contains gold.
2. If Chest A contains gold, then chest C
contains clay.
3. If chest B contains clay then chest A
contains gold.
Which chest if any can be labelled as to its
content?
Misleading Labels 4
Logic II
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The possible scenarios are the following.
1 2 3 4 5 6 7 8
A G G G G C C C C
B G G C C G G C C
C G C G C G C G C
The table exhausts every possibility. A G on row A means
that chest A contains gold, while a C on row A means
that chest A contains clay. For instance column 2, means
that chest A contains gold, chest B contains gold and
chest C contains clay.
J.M.Basilla
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Sample Logic
Problems
Problem 1
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
Misleading Labels 4
Logic II
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The possible scenarios are the following.
1 2 3 4 5 6 7 8
A G G G G C C C C
B G G C C G G C C
C G C G C G C G C
J.M.Basilla
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Sample Logic
Problems
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Hence, columns 4 and 8 are not possible.
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
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A C on row C implies a G on row B.
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If chest C contains clay then chest B contains
gold.
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Problem 1
Misleading Labels 4
Logic II
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The possible scenarios are the following.
1 2 3 4 5 6 7 8
A G G G
C C C
G G C
B G G C
C G C G
G C G
J.M.Basilla
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Sample Logic
Problems
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Hence, columns 1 and 3 are not possible.
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
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A G on row A implies a C on row C.
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If Chest A contains gold, then chest C contains
clay.
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Problem 1
Misleading Labels 4
Logic II
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The possible scenarios are the following.
1 2 3 4 5 6 7 8
A
G
C C C
G
G G C
B
C
C
G C G
J.M.Basilla
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Sample Logic
Problems
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Hence, columns 7 is not possible.
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A C on row B implies a G on row A.
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
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If chest B contains clay then chest A contains
gold.
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Problem 1
Misleading Labels 4
Logic II
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The possible scenarios are the following.
1 2 3 4 5 6 7 8
A
G
C C
G
G G
B
C
C
G C
J.M.Basilla
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Sample Logic
Problems
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Row A still contains G and C
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Problem 1
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Row C still contains G and C
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Hence Chest B has no other choice but to contain
gold. On the other hand, we do not have enough
information to determine the content of chest A and
C.
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Problem 3
More Logic Problem
Last Semester’s
Quiz
Row B still contains G only.
JB
Problem 2
Knights, Normal and Spy I
Logic II
J.M.Basilla
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It is known that knights always tell the truth, spies
always lie and normal people sometimes lie and
sometimes tell the truth.
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Problem 1
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Sample Logic
Problems
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Which one is the knight, the spy and the normal?
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Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
1. It is known that one of them is spy, one of them is a
knight, and one of them is normal.
JB
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Three individuals, Alvin, Theodore and Roosevelt
where captured and were interrogated.
Alvin: Theodore is not a spy.
Roosevelt: Alvin is not a knight.
Theodore: Roosevelt is a knight.
Argument
Solution
Logic II
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Problem 1
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Therefore, Theodore cannot be the knight.
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Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
then Roosevelt is also a knight as
Inductive vs Deductive
Reasoning
Sample Logic
Problems
8
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then Theodore’s statement is true
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Argument
Common forms of
Deductive Reasoning
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Normal
Theodore
Roosevelt
Theodore
Alvin
Roosevelt
Alvin
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Knight
Spy
Alvin
Roosevelt
Alvin
Theodore
Roosevelt
Alvin
Roosevelt Theodore
Theodore
Alvin
Theodore Roosevelt
If Theodore is the knight
Solution
Logic II
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Problem 1
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Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
then Theodore is also a spy JB
Inductive vs Deductive
Reasoning
Sample Logic
Problems
8
8
then Alvin’s statement is false
Therefore, Alvin cannot be the spy.
Argument
Common forms of
Deductive Reasoning
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8
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Normal
Theodore
Roosevelt
Theodore
Alvin
Roosevelt
Alvin
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Knight
Spy
Alvin
Roosevelt
Alvin
Theodore
Roosevelt
Alvin
Roosevelt Theodore
Theodore
Alvin
Theodore Roosevelt
If Alvin is the spy
Solution
Logic II
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Problem 1
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Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
then Theodore is either a knight or normal.
JB
Inductive vs Deductive
Reasoning
Sample Logic
Problems
then Theodore’s statement is true
Therefore, Theodore cannot be the spy.
Argument
Common forms of
Deductive Reasoning
JB
as
lla
JB
as
as
i
8
8
8
8
illa
J.M.Basilla
illa
Normal
Theodore
Roosevelt
Theodore
Alvin
Roosevelt
Alvin
JB
illa
JB
as
lla
as
i
JB
JB
as
i
lla
JB
a
si
lla
Knight
Spy
Alvin
Roosevelt
Alvin
Theodore
Roosevelt
Alvin
Roosevelt Theodore
Theodore
Alvin
Theodore Roosevelt
If Roosevelt is the knight
Solution
Logic II
illa
JB
as
illa
JB
as
JB
as
illa
Problem 1
illa
JB
as
JB
as
as
JB
JB
as
illa
as
JB
illa
JB
as
i
JB
illa
as
JB
illa
illa
as
illa
lla
illa
JB
as
Therefore, Theodore is the normal and Roosevelt is the
spy.
illa
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
then Theodore cannot be the spy.
as
Inductive vs Deductive
Reasoning
Sample Logic
Problems
then Alvin’s statement is true.
JB
Argument
Common forms of
Deductive Reasoning
illa
3
8
8
8
8
8
J.M.Basilla
JB
as
JB
as
i
lla
JB
as
illa
illa
JB
as
lla
as
i
JB
JB
as
i
lla
JB
a
si
lla
Knight
Spy
Normal
Alvin
Roosevelt Theodore
Alvin
Theodore Roosevelt
Roosevelt
Alvin
Theodore
Roosevelt Theodore
Alvin
Theodore
Alvin
Roosevelt
Theodore Roosevelt
Alvin
Therefore, Alvin is the knight.
Knights, Normal and Spy II
Logic II
illa
JB
as
illa
JB
as
JB
as
illa
illa
JB
as
JB
a
si
lla
It is known that knights always tell the truth, spies
always lie and normal people sometimes lie and
sometimes tell the truth.
J.M.Basilla
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Three individuals, Alvin, Theodore and Roosevelt
where captured and were interrogated.
Sample Logic
Problems
illa
JB
as
illa
JB
as
lla
as
i
JB
lla
as
i
JB
JB
as
i
lla
Problem 1
It is known that one of them is spy, one of them is a
knight, and one of them is normal.
illa
illa
JB
as
illa
as
JB
JB
as
illa
illa
as
JB
JB
as
illa
Which one is the knight, the spy and the normal?
Problem 3
More Logic Problem
Last Semester’s
Quiz
JB
as
illa
JB
as
as
illa
JB
lla
as
i
JB
JB
as
illa
Alvin: Roosevelt is a normal and his statement is
true.
Roosevelt: I am normal.
Theodore: Roosevelt is normal or his statement is
false.
Problem 2
Solution
Logic II
JB
as
illa
JB
as
illa
JB
as
JB
as
as
i
illa
Problem 1
illa
illa
JB
as
as
JB
JB
as
illa
as
JB
illa
JB
as
i
JB
illa
as
JB
JB
as
illa
as
illa
lla
illa
JB
as
Therefore, Roosevelt cannot be the knight.
illa
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
then Roosevelt is the normal. as
Inductive vs Deductive
Reasoning
Sample Logic
Problems
then Roosevelt’s statement is true.
JB
Argument
Common forms of
Deductive Reasoning
lla
JB
as
8
8
illa
J.M.Basilla
illa
Normal
Theodore
Roosevelt
Theodore
Alvin
Roosevelt
Alvin
JB
illa
JB
as
lla
as
i
JB
JB
as
i
lla
JB
a
si
lla
Knight
Spy
Alvin
Roosevelt
Alvin
Theodore
Roosevelt
Alvin
Roosevelt Theodore
Theodore
Alvin
Theodore Roosevelt
If Roosevelt is the knight
Solution
Logic II
illa
illa
JB
as
JB
as
as
i
JB
as
JB
as
Problem 1
illa
illa
JB
as
illa
JB
as
as
JB
as
JB
JB
as
illa
illa
as
JB
illa
as
illa
JB
lla
as
i
JB
illa
as
JB
illa
as
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
then Roosevelt is not normal and his statement is
true. JB
Inductive vs Deductive
Reasoning
Sample Logic
Problems
then Theodore’s statement is false
Therefore, Theodore cannot be the spy.
Argument
Common forms of
Deductive Reasoning
illa
8
8
8
illa
J.M.Basilla
lla
JB
as
illa
Normal
Theodore
Roosevelt
Theodore
Alvin
Roosevelt
Alvin
JB
illa
JB
as
lla
as
i
JB
JB
as
i
lla
JB
a
si
lla
Knight
Spy
Alvin
Roosevelt
Alvin
Theodore
Roosevelt
Alvin
Roosevelt Theodore
Theodore
Alvin
Theodore Roosevelt
If Theodore is the spy
Solution
Logic II
illa
illa
JB
as
JB
as
as
i
JB
JB
as
JB
as
Problem 1
illa
illa
JB
as
illa
as
JB
JB
as
illa
illa
as
JB
JB
as
illa
JB
as
as
illa
JB
lla
as
i
JB
illa
as
JB
illa
Therefore, Roosevelt cannot be the normal.
as
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
then Alvin and Theodore’s statement are both true.
JB
Inductive vs Deductive
Reasoning
Sample Logic
Problems
then Roosevelt’s statement is true
then no one can be the spy. Argument
Common forms of
Deductive Reasoning
illa
8
8
8
8
illa
J.M.Basilla
lla
JB
as
illa
illa
JB
as
lla
as
i
JB
JB
as
i
lla
JB
a
si
lla
Knight
Spy
Normal
Alvin
Roosevelt Theodore
Alvin
Theodore Roosevelt
Roosevelt
Alvin
Theodore
Roosevelt Theodore
Alvin
Theodore
Alvin
Roosevelt
Theodore Roosevelt
Alvin
If Roosevelt is the normal
Solution
Logic II
illa
JB
as
illa
JB
as
JB
as
illa
Problem 1
illa
illa
JB
as
illa
JB
as
as
JB
JB
as
illa
as
JB
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
illa
as
illa
JB
lla
as
i
JB
illa
as
JB
illa
JB
as
illa
then Alvin is the normal and Theodore is the knight.
as
Inductive vs Deductive
Reasoning
Sample Logic
Problems
then Alvin’s statement is false while Theodore’s
statement is true .
JB
Argument
Common forms of
Deductive Reasoning
illa
8
8
8
8
8
3
J.M.Basilla
JB
as
JB
as
i
lla
JB
as
illa
illa
JB
as
lla
as
i
JB
JB
as
i
lla
JB
a
si
lla
Knight
Spy
Normal
Alvin
Roosevelt Theodore
Alvin
Theodore Roosevelt
Roosevelt
Alvin
Theodore
Roosevelt Theodore
Alvin
Theodore
Alvin
Roosevelt
Theodore Roosevelt
Alvin
Therefore, Roosevelt is the spy.
Knights, Normal and Spy III
Logic II
J.M.Basilla
illa
JB
as
illa
JB
as
JB
as
illa
illa
JB
as
JB
a
si
lla
It is known that knights always tell the truth, spies
always lie and normal people sometimes lie and
sometimes tell the truth.
JB
as
illa
Problem 1
illa
JB
as
lla
as
i
JB
JB
as
i
lla
lla
as
i
JB
Sample Logic
Problems
illa
JB
as
illa
JB
as
as
illa
JB
lla
as
i
JB
JB
as
illa
Alvin: Roosevelt is a spy.
Roosevelt: Alvin is a knight.
Theodore: Either Alvin or Roosevelt is telling the
truth.
illa
JB
as
illa
JB
as
illa
as
JB
JB
as
illa
Which one is the knight, the spy and the normal?
illa
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
It is known that at least one of the three is a knight.
as
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Three individuals, Alvin, Theodore and Roosevelt
where captured and were interrogated.
JB
Argument
Solution
illa
JB
as
illa
JB
as
JB
as
illa
Problem 1
illa
illa
JB
as
illa
as
JB
as
JB
JB
as
illa
JB
as
JB
as
i
JB
illa
as
JB
illa
as
illa
lla
illa
JB
as
Therefore, Alvin cannot be the knight.
illa
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
then Roosevelt’s statement is true. as
Inductive vs Deductive
Reasoning
Sample Logic
Problems
then Roosevelt is a spy.
JB
Argument
Common forms of
Deductive Reasoning
JB
as
8
8
illa
illa
Logic II
J.M.Basilla
lla
JB
as
as
i
JB
illa
JB
as
lla
as
i
Normal
Theodore
Roosevelt
Theodore
Alvin
Roosevelt
Alvin
JB
JB
as
i
lla
JB
a
si
lla
Knight
Spy
Alvin
Roosevelt
Alvin
Theodore
Roosevelt
Alvin
Roosevelt Theodore
Theodore
Alvin
Theodore Roosevelt
If Alvin is the knight
Solution
Logic II
illa
illa
JB
as
JB
as
as
i
JB
as
illa
JB
as
Problem 1
illa
illa
JB
as
as
JB
JB
as
illa
as
JB
illa
JB
as
i
JB
illa
as
JB
JB
as
illa
as
illa
lla
illa
JB
as
Therefore, Roosevelt cannot be the knight.
illa
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
then Alvin’s statement is true. as
Inductive vs Deductive
Reasoning
Sample Logic
Problems
then Alvin is also a knight.
JB
Argument
Common forms of
Deductive Reasoning
illa
8
8
8
8
J.M.Basilla
lla
JB
as
illa
Normal
Theodore
Roosevelt
Theodore
Alvin
Roosevelt
Alvin
JB
illa
JB
as
lla
as
i
JB
JB
as
i
lla
JB
a
si
lla
Knight
Spy
Alvin
Roosevelt
Alvin
Theodore
Roosevelt
Alvin
Roosevelt Theodore
Theodore
Alvin
Theodore Roosevelt
If Roosevelt is the knight
Solution
Logic II
illa
illa
JB
as
JB
as
as
i
JB
JB
as
illa
JB
as
Problem 1
illa
illa
JB
as
illa
as
illa
as
JB
JB
as
illa
illa
as
JB
JB
JB
as
i
JB
JB
as
as
illa
lla
illa
as
JB
as
illa
Then Alvin is normal and Roosevelt is a spy.
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
But Roosevelt’s statement is already false.
JB
Inductive vs Deductive
Reasoning
Sample Logic
Problems
then Alvin or Roosevelt’s statement is true.
then Alvin’s statement is true.
Argument
Common forms of
Deductive Reasoning
illa
8
8
8
8
8
J.M.Basilla
lla
JB
as
illa
illa
JB
as
lla
as
i
JB
JB
as
i
lla
JB
a
si
lla
Knight
Spy
Normal
Alvin
Roosevelt Theodore
Alvin
Theodore Roosevelt
Roosevelt
Alvin
Theodore
Roosevelt Theodore
Alvin
Theodore
Alvin
Roosevelt
Theodore Roosevelt
Alvin
Therefore, Theodore is the knight.
Solution
Logic II
illa
JB
as
illa
JB
as
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Sample Logic
Problems
JB
as
illa
Problem 1
illa
8
8
8
8
8
3
J.M.Basilla
JB
as
as
i
lla
JB
as
illa
Normal
Theodore
Roosevelt
Theodore
Alvin
Roosevelt
Alvin
JB
as
i
lla
JB
as
illa
Spy
Roosevelt
Theodore
Alvin
Theodore
Alvin
Roosevelt
JB
JB
as
i
lla
JB
a
si
lla
Knight
Alvin
Alvin
Roosevelt
Roosevelt
Theodore
Theodore
Problem 2
Problem 3
More Logic Problem
illa
illa
JB
as
illa
JB
as
as
JB
JB
as
illa
as
JB
illa
as
illa
JB
lla
as
i
JB
illa
as
JB
JB
as
illa
JB
as
illa
Last Semester’s
Quiz
Red and Blue Hats
Logic II
illa
JB
as
illa
Problem 1
illa
illa
JB
as
illa
JB
as
as
JB
JB
as
illa
as
JB
Sample Logic
Problems
illa
JB
JB
illa
as
JB
JB
illa
as
Inductive vs Deductive
Reasoning
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
What colour hat is each man wearing?
JB
Argument
Common forms of
Deductive Reasoning
illa
JB
as
lla
as
i
JB
as
illa
as
i
as
i
as
lla
JB
as
i
A: I see 4 blue hats.
B: I see 3 blue hats and 1 red hat.
C: I see 1 blue hat and 3 red hats.
D: I see 4 red hats.
E: (did not say anything)
illa
JB
lla
lla
JB
a
Five men are wearing blue or red hats. A man
wearing a blue hat always tells the truth. A man
wearing a red hat always lie. They look at each
others hat and said.
JB
as
illa
JB
as
JB
as
illa
illa
JB
as
si
lla
J.M.Basilla
Solution
If A wears a blue hat
Logic II
J.M.Basilla
illa
JB
as
JB
as
JB
as
illa
illa
illa
C
JB
as
JB
a
si
lla
B
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
A
Sample Logic
Problems
illa
illa
JB
as
E
JB
as
as
i
lla
Problem 1
JB
lla
as
i
JB
JB
as
i
lla
D
Problem 2
Problem 3
More Logic Problem
illa
JB
as
illa
as
JB
JB
as
illa
illa
as
JB
JB
as
illa
A must be wearing a red hat and at most 3
persons wears a blue cap.
JB
as
illa
true
false false
false
JB
as
as
illa
JB
lla
as
i
JB
JB
as
illa
A:I see 4 blue hats.
B:I see 3 blue hats and 1 red hat.
C:I see 1 blue hat and 3 red hats.
D: I see 4 red hats.
illa
Last Semester’s
Quiz
Solution
If B wears a blue hat given A wears a red one.
Logic II
J.M.Basilla
illa
JB
as
JB
as
JB
as
illa
illa
illa
C
JB
as
JB
a
si
lla
B
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
A
Sample Logic
Problems
illa
illa
JB
as
E
JB
as
as
i
lla
Problem 1
JB
lla
as
i
JB
JB
as
i
lla
D
Problem 2
Problem 3
More Logic Problem
illa
JB
as
illa
as
JB
JB
as
illa
illa
as
JB
JB
as
illa
B must be wearing a red hat, and at most 2
people other than A and B wear blue hats.
JB
as
illa
false
true
false false JB
as
as
illa
JB
lla
as
i
JB
JB
as
illa
A:I see 4 blue hats.
B:I see 3 blue hats and 1 red hat.
C:I see 1 blue hat and 3 red hats.
D: I see 4 red hats.
illa
Last Semester’s
Quiz
Solution
A and B wear red hats and if D a blue hat
Logic II
J.M.Basilla
illa
JB
as
JB
as
JB
as
illa
illa
illa
C
JB
as
JB
a
si
lla
B
illa
JB
as
illa
JB
as
lla
as
i
E
JB
lla
as
i
JB
Sample Logic
Problems
Problem 1
D
lla
as
i
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
A
JB
Argument
Problem 2
Problem 3
More Logic Problem
illa
JB
as
illa
as
JB
JB
as
illa
illa
as
JB
JB
as
illa
D must be wearing a red hat, and at most 3
people among A, B, C and E wear red hats.
JB
as
illa
false
false
true true
JB
as
as
illa
JB
lla
as
i
JB
JB
as
illa
A:I see 4 blue hats.
B:I see 3 blue hats and 1 red hat.
C:I see 1 blue hat and 3 red hats.
D: I see 4 red hats.
illa
Last Semester’s
Quiz
Solution
A, B and D wear red hats.
Logic II
illa
JB
as
JB
as
JB
as
illa
illa
illa
C
JB
as
JB
a
si
lla
B
J.M.Basilla
Sample Logic
Problems
illa
JB
as
illa
E
JB
as
as
i
lla
Problem 1
JB
lla
as
i
JB
JB
as
i
lla
D
illa
JB
as
illa
JB
as
as
illa
lla
as
i
illa
as
illa
as
JB
JB
as
illa
as
JB
illa
JB
JB
illa
as
JB
JB
is false.
So E must also be red.
This contradicts, ”I see four red hats .” is false
C must wear a blue hat and therefore E wears also a
blue hat.
illa
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
If C wears red hat, the statement
”I see one blue hat and 3 red hats,”
as
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
A
JB
Argument
The correct answer
Logic II
illa
JB
as
illa
illa
JB
as
C
B
JB
as
illa
JB
as
JB
a
si
lla
J.M.Basilla
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Sample Logic
Problems
A
illa
JB
as
illa
JB
as
lla
as
i
D
JB
lla
as
i
JB
JB
as
i
lla
Problem 1
E
illa
illa
JB
as
as
JB
as
JB
JB
as
illa
JB
as
illa
false
false
true
false
illa
as
illa
JB
lla
as
i
JB
illa
as
JB
illa
as
JB
illa
as
Problem 3
More Logic Problem
Last Semester’s
Quiz
A:I see 4 blue hats.
B:I see 3 blue hats and 1 red hat.
C:I see 1 blue hat and 3 red hats.
D: I see 4 red hats.
JB
Problem 2
Who stole the bread?
problem 1
Logic II
illa
JB
as
illa
Problem 1
illa
Problem 2
Problem 3
More Logic Problem
illa
Last Semester’s
Quiz
illa
JB
as
JB
as
Inductive vs Deductive
Reasoning
Sample Logic
Problems
JB
as
illa
JB
as
illa
as
JB
Argument
Common forms of
Deductive Reasoning
illa
JB
as
lla
as
i
JB
as
illa
JB
lla
as
i
lla
as
i
JB
illa
as
JB
JB
as
illa
JB
as
illa
JB
JB
as
i
lla
One of the three elves, Arn, Birn and Con was
known to have pilfered and eaten two loaves of
bread all by himself. The three made
statements:
Arn: I stole the bread.
Birn: Arn is not telling the truth,
Con : Birn stole the bread.
It is known that the thief made a false statement.
JB
as
illa
JB
as
JB
as
illa
illa
JB
as
JB
a
si
lla
J.M.Basilla
Who stole the bread?
problem 1 - solution
Logic II
Let
J.M.Basilla
illa
JB
as
JB
as
Inductive vs Deductive
Reasoning
Sample Logic
Problems
JB
as
JB
as
illa
Problem 1
Problem 2
Problem 3
More Logic Problem
illa
JB
as
as
JB
JB
as
illa
JB
as
illa
illa
Last Semester’s
Quiz
illa
as
JB
Argument
Common forms of
Deductive Reasoning
lla
as
i
JB
as
illa
JB
lla
as
i
lla
as
i
JB
illa
as
JB
JB
as
illa
JB
as
illa
JB
JB
as
i
lla
r: (Con) Birn stole the bread.
p T T T T F F F F
q T T F F T T F F
r T F T F T F T F
8 8 8 8 8 3 8 8
illa
JB
as
JB
as
JB
a
q: (Birn) Arn is not telling the truth,
illa
illa
illa
si
lla
p:(Arn) I stole the bread.
Who stole the bread?
problem 1 - solution
Logic II
If p is true
illa
JB
as
JB
as
illa
illa
JB
as
JB
as
illa
then Arn is the thief.
then Arn lies. si
lla
JB
a
J.M.Basilla
Therefore p is false.
Sample Logic
Problems
illa
JB
as
illa
JB
as
lla
as
i
JB
Problem 1
JB
as
i
lla
lla
as
i
JB
Hence, r is false.
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Hence, q is true.
Birn cannot be the thief.
Argument
Problem 2
Problem 3
More Logic Problem
illa
illa
JB
as
illa
JB
as
as
JB
JB
as
illa
as
JB
illa
as
illa
JB
lla
as
i
JB
illa
as
JB
JB
as
illa
JB
as
illa
Last Semester’s
Quiz
Who stole the bread?
problem 1 - solution
Logic II
Therefore
J.M.Basilla
JB
as
JB
as
JB
as
JB
a
illa
”q: (Birn) Arn is not telling the truth,” is true.
JB
as
illa
illa
illa
si
lla
”p:(Arn) I stole the bread,” is false.
Sample Logic
Problems
JB
as
JB
as
as
i
JB
JB
as
i
Since Arn cannot be the thief, then Con is the thief.
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Problem 1
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Then Arn or Con is the thief.
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Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
”r: (Con) Birn stole the bread,” is false.
JB
Argument
Problem 2
Problem 3
More Logic Problem
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Last Semester’s
Quiz
Who stole the bread?
Problem-2
Logic II
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J.M.Basilla
Sample Logic
Problems
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Problem 1
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Arn: Either Brin is guilty or Con is guilty.
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Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
Brin: I am not guilty.
Con : Arn is not guilty..
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
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It was known that exactly one of the three is guilty and
only one of the three statements made(given below) is
true. It was Not known however whether the true
statement was made by the thief or not.
Argument
Who stole the bread?
Problem 2-Solution
Logic II
Let
J.M.Basilla
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Problem 1
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Problem 2
Problem 3
More Logic Problem
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Last Semester’s
Quiz
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Inductive vs Deductive
Reasoning
Sample Logic
Problems
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Argument
Common forms of
Deductive Reasoning
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r: (Con) Arn is not guilty.
p T T T T F F F F
q T T F F T T F F
r T F T F T F T F
8 8 8 8 8 3 8 8
Only one of the the three statements is true.
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q: (Birn) I am not guilty.
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p: (Arn) Either Birn is guilty or Con is guilty.
Who stole the bread?
Problem 2-Solution
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1. Then Birn and Arn are guilty. JB
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T T T T F F F F
T T F F T T F F
T F T F T F T F
8 8 8 8 8 3 8 8
Only one of the the three statements is true.
If ”q: (Birn) I am not guilty,” and ”r: (Con) Arn is not guilty,”
are both false.
Logic II
J.M.Basilla
Argument
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
Sample Logic
Problems
Problem 1
Problem 2
Problem 3
More Logic Problem
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Last Semester’s
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Who stole the bread?
Problem 2-Solution
Logic II
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Problem 1
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Inductive vs Deductive
Reasoning
Sample Logic
Problems
”Birn is not guilt(from not p)” and Birn is guilty (from
not q).
Therefore, p and q cannot be simultaneously false.
Therefore, p is true and q and r are false.
Argument
Common forms of
Deductive Reasoning
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T T T T F F F F
T T F F T T F F
T F T F T F T F
8 8 8 8 8 3 8 8
Only one of the the three statements is true.
If ” p: (Arn) Either Birn is guilty or Con is guilty,” and ”q:
(Birn) I am not guilty,” are both false
p
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Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
Who stole the bread?
Problem 2-Solution
Logic II
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T T T T F F F F
T T F F T T F F
T F T F T F T F
8 8 8 8 8 3 8 8
Only one of the the three statements is true.
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”r: (Con) Arn is not guilty, is false.
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Sample Logic
Problems
Problem 1
Problem 2
Problem 3
More Logic Problem
Last Semester’s
Quiz
Therefore, Arn is the thief.
JB
Inductive vs Deductive
Reasoning
Common forms of
Deductive Reasoning
”p: (Arn) Either Birn is guilty or Con is guilty,” is false.
”q: (Birn) I am not guilty,” is true.
Argument