Section 2-2: Conditional Statements

Rigor: Identify the hypothesis and conclusion of a conditional statement; state truth values and counterexamples

Relevance: Logical reasoning

Explore logic with Venn diagrams

Turn to page 57 Explore #1

Vocab: Conditional Statements

p q~P means NOT P

Conditional statement – an if –then statement

Hypothesis – the part p following if.

Conclusion – the part q following then.

Conjecture – a statement you believe to be

true based on observed patterns

Identify the hypothesis and conclusion for each bumper sticker

1. If you follow me too closely, then I will flick a booger on your windshield.

2. If the rapture happens, then this car will have no driver.

Writing a conditional statement

Step 1: Identify hypothesis and conclusion

Step 2: Write “if…, then…” statement. Don’t forget to use a noun before the pronoun!

Example 1:

Write “Vertical angles are congruent.” as a conditional.

Step 1: box hypothesis, underline conclusion

Step 2:

Example 2:

Write “Dolphins are mammals.” as a conditional.

Truth Values

Conditional statements can be either TRUE or FALSE.

True Statements: If the hypothesis is true, the conclusion MUST ALWAYS be true

Counter Examples

Counter Example – an example that proves a statement is false.

You only need 1 counter example to prove a statement false!

Example: T or F? Give a counterexample for if statement is F.

1. If a woman is born in FL, then she is American.

2. If a number is divisible by 3, then it is odd.

Example: T or F? Give a counterexample for if statement is F.

3. If a month has 28 days, then it is February.

4. If two angles form a linear pair, then they are supplementary.

Video: How many examples of bad logic can you spot?

http://www.youtube.com/watch?v=zrzMhU_4m-g

Another type of logic statement

Converse – “If q, then p”

- flip the if and then parts of a conditional statement

Example:

Conditional:

Converse:

Truth values don’t have to be the same for both logic statements!

“If I play soccer, then I’m an athlete.”

1. What is the converse to this conditional?

2. What are the truth values of each?

“If a polygon is a square, then it is a rectangle”

1. What is the converse of the conditional statement?

2. What are the truth values of each?

“If the shape has 3 angles, then it is a triangle.”

1. What is the converse of the conditional statement?

2. What is the truth value of each?

2-2 Classwork

Heading: CW 2-2 textbook pg 85-86

Problems #14 – 20, 38 – 40 For #38-40 write the converse of each

statement AND list a counterexample

2 – 2 Homework

From the core book

pg 59 #1 – 4, 6 – 10 (do not do inverses or contrapositives)

Pg 60 # 1, 6 (do not do inverses or contrapositives)

What is your example of a conditional statement and converse?

Crazy Converses!

Conditional ConverseStatement

True or False? True or False?

Must illustrate statement and converse.