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

2. Explore logic with Venn diagrams
Turn to page 57 Explore #1

3. Making Conjectures
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.

4. 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

5. 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.

6. 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!

7. Example 1: Write “Vertical angles are congruent.” as a conditional.
Step 1: box hypothesis, underline conclusion
Step 2:

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

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

10. Counter Examples
Counter Example – an example that proves a statement is false.
You only need 1 counter example to prove a statement false!

11. 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.

12. 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.

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

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

15. Example:
Conditional:
Converse:
Truth values don’t have to be the same for both logic statements!

16. “If I play soccer, then I’m an athlete.”
What is the converse to this conditional?
What are the truth
values of each?

17. “If a polygon is a square, then it is a rectangle”
What is the converse of the conditional statement?
What are the truth values of each?

18. “If the shape has 3 angles, then it is a triangle.”
What is the converse of the conditional statement?
What is the truth value of each?

19. 2 – 2 Assignment from the Workbook
pg 59 #1 – 4, 6 – 10
(do not do inverses or contrapositives)
Pg 60 # 1, 6
Due Wednesday (periods 2, 4, & 6)
Due Thursday (periods 1, 5, & 7)

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