Warm up

1. Warm up

2. Logic Unit 1 Lesson 9

3. 4 Corners Activity5 minute time limit… • Find three other people to work with and answer the following questions. Post answers on the 4 posters located around the room. Finish the following statements: • If you eat lunch at school then,… • If you get an A in Geometry then,… • Is school started later in the day then,… • If I would have a positive attitude then,…

4. Conditional Statements • A conditional statement is a statement written in “if-then” form. • pq Example: If you study, then you will pass. • Conditional statements have two parts: • Hypothesis ( follows the “if”) • Conclusion ( follows the “then”)

5. Examples Example 1: Consider the statement “If you study, then you will pass.” Hypothesis: you study Conclusion: you will pass Example 2: If it is raining, then we will read a book. Hypothesis: Conclusion:

6. Other forms of conditional statements • Example: All lines are straight. “If –then” form: If a figure is a line, then it is straight. • Rewrite these conditional statements in “if-then” form. • All triangles have three sides. • All dogs bark.

7. Converse of a conditional statement • The converse of a statement is formed by switching the hypothesis and the conclusion. • q p • This is much easier to do when a statement is in “if-then” form. Example: If today is Saturday, then there is no school. Hypothesis: Conclusion: Converse:

8. If-Then Form Fun  • Write the statements in if-then form on the back of each card. • Underline the hypothesis once, the conclusion twice. • Pass your stack of cards to the person to your right. Have them check your work. • Continue passing and checking until you receive your original cards back. • How did you do?

9. Pairs activity • Choose a partner. • Read the passage from Alice’s Adventures in Wonderland from the task. Stop when you finish the short passage. • Complete #1-6 with your partner. • Wait silently while everyone gets finished.

10. Truth Value and Equivalence • Look at the conditional to determine whether it is true or false • Do the same with the converse of the conditional • Any statement can be true or false, so you must consider both cases. • If both parts are true OR both parts are false, then they are logically equivalent. • If one is false and the other is true, then they are not logically equivalent.

11. Examples • If the animal flies, then it must be a bird. • Is this statement true? Can you think of any other animal that flies? Think of an animal that flies that is NOT a bird. • Now, find the converse of the conditional. • If the animal is a bird, then it must fly. • Is this statement true? What about an ostrich or a penguin? • This conditional and its converse is not logically equivalent.

12. Absolute Value Functions • With your partner, complete #10-13 on the Wonderland to Functionland task using the equation f(x) = |x|

13. Inverse of a statement • A statement formed by negating the hypothesis and conclusion of a conditional statement. • p q Example: If it is sunny, then we will play outside. Inverse: If it is not sunny, then we will not play outside. Example: If you do not cry, then you will get a treat. Inverse:

14. Contrapositive • Formed by negating the hypothesis and conclusion of the converse. • q p • Example: Conditional: If I am happy, then I will smile. Converse: Contrapositive:

15. Back to Functionland! • Complete #16 -17 from the Functionland task • Be prepared to share your answers with the class!

16. One Last Thing… • Biconditional statements are those that the statement and its converse are BOTH true • Always contains the phrase “if and only if”

17. Conditional StatementsGraphic Organizer (Attach #5) • On your own, Find the converse, the inverse, and the contrapositive of the statement given. • When you are finished, turn your paper over and come up with the following: • An if-then statement • Its converse • Its inverse • Its contrapositive