Section 2 2 Conditional Statements Rigor Identify the

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Section 2 -2: Conditional Statements Rigor: Identify the hypothesis and conclusion of a conditional

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 o Turn to page 57 Explore #1

Explore logic with Venn diagrams o Turn to page 57 Explore #1

Making Conjectures o Conjecture – a statement you believe to be true based on

Making Conjectures o Conjecture – a statement you believe to be true based on observed patterns. Make a conjecture about the number of triangles formed compared to the number of sides.

Vocab: Conditional Statements Conditional statement – an if –then statement Hypothesis – the part

Vocab: Conditional Statements Conditional statement – an if –then statement Hypothesis – the part p following if. Conclusion – the part q following then. p q ~P means NOT P

Identify the hypothesis and conclusion for each bumper sticker 1. If you follow me

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 o. Step 1: Identify hypothesis and conclusion o. Step 2:

Writing a conditional statement o. Step 1: Identify hypothesis and conclusion o. 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

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.

Example 2: Write “Dolphins are mammals. ” as a conditional.

Truth Values o Conditional statements can be either TRUE or FALSE. o True Statements:

Truth Values o Conditional statements can be either TRUE or FALSE. o True Statements: If the hypothesis is true, the conclusion MUST ALWAYS be true

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

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

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

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?

Video: How many examples of bad logic can you spot? http: //www. youtube. com/watch? v=zrz. M h. U_4 m-g

Another type of logic statement Converse – “If q, then p” - flip the

Another type of logic statement Converse – “If q, then p” - flip the if and then parts of a conditional statement

Example: o Conditional: o Converse: o Truth values don’t have to be the same

Example: o Conditional: o Converse: o 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

“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

“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

“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 Assignment from the Workbook o pg 59 #1 – 4, 6

2 – 2 Assignment from the Workbook o pg 59 #1 – 4, 6 – 10 (do not do inverses or contrapositives) o Pg 60 # 1, 6 (do not do inverses or contrapositives) o Due Wednesday (periods 2, 4, & 6) o Due Thursday (periods 1, 5, & 7)

What is your example of a conditional statement and converse? Crazy Converses! Conditional Statement

What is your example of a conditional statement and converse? Crazy Converses! Conditional Statement True or False? Converse True or False? Must illustrate statement and converse.