2.1­2.2 HN Inductive Reasoning and Conditional Statements.notebook
September 19, 2016
Get out the class work from last class. Start to check answers with your partner(s). Discuss any questions where your answers are not the same.
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2.1­2.2 HN Inductive Reasoning and Conditional Statements.notebook
September 19, 2016
Supplement of <A
Complement of <B
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2.1­2.2 HN Inductive Reasoning and Conditional Statements.notebook
September 19, 2016
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2.1­2.2 HN Inductive Reasoning and Conditional Statements.notebook
September 19, 2016
2.1 Inductive Reasoning
Gathering information (from observation) that can be used to make a general conclusion. When do we use inductive reasoning?
When we are given information that shows us a pattern
** SPECIFIC to GENERAL **
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2.1­2.2 HN Inductive Reasoning and Conditional Statements.notebook
September 19, 2016
After we use inductive reasoning we come to a conclusion. That conclusion is called a conjecture.
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2.1­2.2 HN Inductive Reasoning and Conditional Statements.notebook
September 19, 2016
Do you think inductive reasoning always results in a true conjecture?
Observation: Mia came to class late this morning.
Observation: Mia’s hair was uncombed.
Observation: Mia is very fussy about her hair.
Conclusion: Mia overslept.
Alternate conclusions?
Disproving Conjectures
To show that a conjecture is false, you only
need to find one COUNTEREXAMPLE.
If it is raining, the sidewalk is wet.
counterexamples?
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•
•
•
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2.1­2.2 HN Inductive Reasoning and Conditional Statements.notebook
September 19, 2016
Find a counterexample:
The sum of two numbers is always greater than the larger number.
Three points on a plane always form a triangle.
Do Now #6 1. Monday, Wednesday, Friday, ...
2. 1, 2, 4, 8, ... 3.
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2.1­2.2 HN Inductive Reasoning and Conditional Statements.notebook
September 19, 2016
Eleusis ­ A Card Game
2.2 Conditional Statements
"If, then" statement
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2.1­2.2 HN Inductive Reasoning and Conditional Statements.notebook
September 19, 2016
If I do my chores, then I get my allowance.
hypothesis (p)
conclusion (q)
Bird
What is the
conditional
statement?
wings
Every conditional statement has a truth value
or either true (T) or false (F).
*** The only time a conditional statement is
false is when the hypothesis is true and the
conclusion is false.
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2.1­2.2 HN Inductive Reasoning and Conditional Statements.notebook
September 19, 2016
Just like inductive reasoning, you only
have to find ONE counterexample to show
that a conditional statement is not true.
If an angle is obtuse, then it has a measure of
100 degrees.
counterexample:
Definition
A conditional statement is a
statement that can be written in
the form "If p, then q."
The CONVERSE is the
statement formed by exchanging
the hypothesis and conclusion.
The INVERSE is the statement
formed by negating the
hypothesis and the conclusion.
The CONTRAPOSITIVE is
the statement formed by both
exchanging and negating the
hypothesis and the conclusion.
Symbols
p
q
q
p
¬p
¬q
¬q
¬p
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2.1­2.2 HN Inductive Reasoning and Conditional Statements.notebook
September 19, 2016
Which is the converse, inverse, contrapositive?
Conditional statement: If this month is August, then the next month is
September.
If the next month is not Septemeber, then this month is not August.
If the next month is September, then this month is August.
If this month is not August, then the next month is not September.
If an insect is a butterfly, then it has two wings.
converse:
inverse:
contrapositive:
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2.1­2.2 HN Inductive Reasoning and Conditional Statements.notebook
September 19, 2016
If, Then Worksheet
What's in a name?
QUIZ NEXT CLASS
Book Work ­ pg. 77 #2,5,8­10
pg. 78 #28,31
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2.1­2.2 HN Inductive Reasoning and Conditional Statements.notebook
September 19, 2016
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