Section 2-2: Conditional Statements Rigor: Identify the hypothesis and conclusion of a conditional statement; state truth values and counterexamples Relevance:

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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? hU_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  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! ConditionalConverse Statement True or False? True or False? Must illustrate statement and converse.