Geometry Pre-AP
BOMLA LACYMATH
10/6
“My logic is undeniable!”
Logic (Chapter 2-2)
Making a Statement
 A statement is any sentence that is true or
false.
Making a Statement
 A statement is any sentence that is true or
false.
 DUH!!!!
Right????
Making a Statement
 A statement is any sentence that is true or
false.
 DUH!!!!
Right????
 They
can either be true or false, but not both.
Whether a statement is true or false is called its
truth value (sometimes called the “validity” of the
statement).
 Statements
as p or q.
are often represented using a letter such
Making a Statement
 True or False???

p: BOMLA is an all boys school.
Making a Statement
 True or False???

p: BOMLA is an all boys school.
p is true!
Making a Statement
 True or False???

q: Mr. Lacy is 28 years old.
Making a Statement
 True or False???

q: Mr. Lacy is 28 years old.
q is false!!! (as of September 26)
Making a Statement
 True or False???

p: Our school has now been open for 6
years.
Making a Statement
 True or False???

p: Our school has now been open for 6
years.
p is true!!!
Making a Statement
 True or False???
 q: You can name a plane using a capital
script letter and 4 non-collinear points.
Making a Statement
 True or False???
 q: You can name a plane using a capital
script letter and 4 non-collinear points.
q is false!!! (It’s 3 non-collinear points.)
“On the contrary…”
 The negation of a statement has the opposite
meaning as well as an opposite truth value.
~p
which is read “not p”
~q
which is read “not q”
Making a Statement

p: BOMLA is an all boys school.
p is true!
~ p: BOMLA is not an all boys school.
Making a Statement

p: BOMLA is an all boys school.
p is true!
~ p: BOMLA is not an all boys school.
~ p is false!
Making a Statement
 q: You can name a plane using a capital
script letter and 4 non-collinear points.
q is false!!! (It’s 3 non-collinear points.)
~ q : You can not name a plane using a
capital script letter and 4 non-collinear
points.
Making a Statement
 q: You can name a plane using a capital
script letter and 4 non-collinear points.
q is false!!! (It’s 3 non-collinear points.)
~ q : You can not name a plane using a
capital script letter and 4 non-collinear
points.
~ q is true!!!
Putting Statements Together
 Compound statement – when two or
more statements are joined together. They
can be joined by the word “or” or the word
“and”.
Putting Statements Together
 Conjunction – joining two or more
statements with “and”

Conjunctions are only true when BOTH statements are true.

Use the symbol ∧ between letters.
Putting Statements Together
 Conjunction – joining two or more
statements with “and”
 Example 1
p: The number 2 is even.
q: The number 2 is prime.
Putting Statements Together
 Conjunction – joining two or more
statements with “and”
 Example 1
p: The number 2 is even.
q: The number 2 is prime.
The number 2 is even, AND the number 2 is prime.
Putting Statements Together
 Conjunction – joining two or more
statements with “and”
 Example 1
p: The number 2 is even.
q: The number 2 is prime.
The number 2 is even, AND the number 2 is prime.
p ∧ q is TRUE!!!
Putting Statements Together
 Conjunction – joining two or more
statements with “and”
 Example 2
p: The number 3 is even.
q: The number 2 is prime.
Putting Statements Together
 Conjunction – joining two or more
statements with “and”
 Example 2
p: The number 3 is even.
q: The number 2 is prime.
The number 3 is even, AND the number 2 is prime.
Putting Statements Together
 Conjunction – joining two or more
statements with “and”
 Example 2
p: The number 3 is even.
q: The number 2 is prime.
The number 3 is even, AND the number 2 is prime.
p ∧ q is FALSE!!!
Putting Statements Together
 Disjunction – joining two or more
statements with “or”

Disjunctions are true when AT LEAST ONE statement is true.

Use the symbol v between letters.
Putting Statements Together
 Disjunction – joining two or more
statements with “or”
 Back to Example 2
p: The number 3 is even.
q: The number 2 is prime.
Putting Statements Together
 Disjunction – joining two or more
statements with “or”
 Back to Example 2
p: The number 3 is even.
q: The number 2 is prime.
The number 3 is even, OR the number 2 is prime.
Putting Statements Together
 Disjunction – joining two or more
statements with “or”
 Back to Example 2
p: The number 3 is even.
q: The number 2 is prime.
The number 3 is even, OR the number 2 is prime.
p v q is TRUE!!!
Putting Statements Together
 Disjunction – joining two or more
statements with “or”
 Example 3
p: Dogs only have 2 legs.
q: Cats lay eggs.
Putting Statements Together
 Disjunction – joining two or more
statements with “or”
 Example 3
p: Dogs only have 2 legs.
q: Cats lay eggs.
Dogs only have 2 legs, OR cats lay eggs.
Putting Statements Together
 Disjunction – joining two or more
statements with “or”
 Example 3
p: Dogs only have 2 legs.
q: Cats lay eggs.
Dogs only have 2 legs, OR cats lay eggs.
p v q is FALSE!!!
Compound
Statement
Determine
truth value of
the Statements
T
Conjunction
Disjunction
Both True?
At Least 1
True?
F
T
F
Compound Statements
 Example 4
p: Mr. Douglas’ first name starts with an “N”.
q: The school day at BOMLA begins at 7am.
Mr. Douglas’ first name starts with an “N”, and the
school day at BOMLA begins at 7am.
p ∧ q is
Mr. Douglas’ first name starts with an “N”, or the school
day at BOMLA begins at 7am.
p v q is
Compound Statements
 Example 4
p: Mr. Douglas’ first name starts with an “N”.
q: The school day at BOMLA begins at 7am.
Mr. Douglas’ first name starts with an “N”, and the
school day at BOMLA begins at 7am.
p ∧ q is FALSE
Mr. Douglas’ first name starts with an “N”, or the school
day at BOMLA begins at 7am.
p v q is
Compound Statements
 Example 4
p: Mr. Douglas’ first name starts with an “N”.
q: The school day at BOMLA begins at 7am.
Mr. Douglas’ first name starts with an “N”, and the
school day at BOMLA begins at 7am.
p ∧ q is FALSE
Mr. Douglas’ first name starts with an “N”, or the school
day at BOMLA begins at 7am.
p v q is TRUE
Compound Statements
 Example 5
p:
q:
r:
9 + 5 = 14
February has 30 days.
A square has four sides.
9 + 5 = 14, and February has 30 days.
9 + 5 = 14, or February has 30 days.
Compound Statements
 Example 5
p:
q:
r:
9 + 5 = 14
February has 30 days.
A square has four sides.
9 + 5 = 14, and February has 30 days.
p ∧ q is
9 + 5 = 14, or February has 30 days.
p v q is
Compound Statements
 Example 5
p:
q:
r:
9 + 5 = 14
February has 30 days.
A square has four sides.
9 + 5 = 14, and February has 30 days.
p ∧ q is FALSE!!!
9 + 5 = 14, or February has 30 days.
p v q is
Compound Statements
 Example 5
p:
q:
r:
9 + 5 = 14
February has 30 days.
A square has four sides.
9 + 5 = 14, and February has 30 days.
p ∧ q is FALSE!!!
9 + 5 = 14, or February has 30 days.
p v q is TRUE!!!
Compound Statements
 Example 5
p:
q:
r:
9 + 5 = 14
February has 30 days.
A square has four sides.
9 + 5 = 14, and a square has four sides.
p ∧ r is
9 + 5 = 14, or a square has four sides.
p v r is
Compound Statements
 Example 5
p:
q:
r:
9 + 5 = 14
February has 30 days.
A square has four sides.
9 + 5 = 14, and a square has four sides.
p ∧ r is TRUE!!!
9 + 5 = 14, or a square has four sides.
p v r is
Compound Statements
 Example 5
p:
q:
r:
9 + 5 = 14
February has 30 days.
A square has four sides.
9 + 5 = 14, and a square has four sides.
p ∧ r is TRUE!!!
9 + 5 = 14, or a square has four sides.
p v r is TRUE!!!
Compound Statements
 Example 5
p:
q:
r:
9 + 5 = 14
February has 30 days.
A square has four sides.
~ p ∧ r is
p ∧ ~ q is
Compound Statements
 Example 5
p:
q:
r:
9 + 5 = 14
February has 30 days.
A square has four sides.
~ p ∧ r is FALSE!!!
p ∧ ~ q is
Compound Statements
 Example 5
p:
q:
r:
9 + 5 = 14
February has 30 days.
A square has four sides.
~ p ∧ r is FALSE!!!
p ∧ ~ q is TRUE!!!
Another Way to Look At Things…
 Conjunctions and Disjunctions can also be
displayed using Venn diagrams.
Another Way to Look At Things…
 Conjunctions and Disjunctions can also be
displayed using Venn diagrams.
Another Way to Look At Things…
 Conjunctions and Disjunctions can also be
displayed using Venn diagrams.
Which section represents ____ ∧ ____ ?
Another Way to Look At Things…
 Conjunctions and Disjunctions can also be
displayed using Venn diagrams.
Which section represents ____ ∧ ____ ?
Which section represents ____ v ______ ?
Another Way to Look At Things…
 A truth table is a method for organizing truth
values of statements. They can be used to determine
the truth values of negations and compound
statements.
Another Way to Look At Things…
 Truth Table
Negation
p
T
F
~p
Another Way to Look At Things…
 Truth Table
Negation
p
~p
T
F
F
Another Way to Look At Things…
 Truth Table
Negation
p
~p
T
F
F
T
Another Way to Look At Things…
 Truth Table
Conjunction
p
q
T
T
T
F
F
T
F
F
p∧q
Another Way to Look At Things…
 Truth Table
Conjunction
p
q
p∧q
T
T
T
T
F
F
T
F
F
Another Way to Look At Things…
 Truth Table
Conjunction
p
q
p∧q
T
T
T
T
F
F
F
T
F
F
Another Way to Look At Things…
 Truth Table
Conjunction
p
q
p∧q
T
T
T
T
F
F
F
T
F
F
F
Another Way to Look At Things…
 Truth Table
Conjunction
p
q
p∧q
T
T
T
T
F
F
F
T
F
F
F
F
Another Way to Look At Things…
 Truth Table
Disjunction
p
q
T
T
T
F
F
T
F
F
pvq
Another Way to Look At Things…
 Truth Table
Disjunction
p
q
pvq
T
T
T
T
F
F
T
F
F
Another Way to Look At Things…
 Truth Table
Disjunction
p
q
pvq
T
T
T
T
F
T
F
T
F
F
Another Way to Look At Things…
 Truth Table
Disjunction
p
q
pvq
T
T
T
T
F
T
F
T
T
F
F
Another Way to Look At Things…
 Truth Table
Disjunction
p
q
pvq
T
T
T
T
F
T
F
T
T
F
F
F
Classwork
CW 02 – My Logic is Undeniable
 Pg. 103
#11-16, 18, 20, 22
 Pg. 104
#23, 31
First 7 minutes individual