Conditional Statements and Deductive Reasoning

1. Chapter 2 Section 3 Conditional Statements

2. Conditional Statements • A conditional statement is a statement that can be written in if-then form. • An if-then statement is written in the form if p, then q. • The phrase immediately following the word if is called the hypothesis. • The phrase immediately following the word then is called the conclusion. • p q, if p then q, or p implies q

3. Hypothesis Conclusion If it is Friday, there is a football game. There is a football game. It is Friday We will have ice cream if you are good. You are good We will have ice cream. Punk rock makes me sick. It is punk rock It makes me sick.

4. Conditional Statements in Disguise Mrs. Limburg is tall. If she is Mrs. Limburg, then she is tall. Perpendicular lines intersect. If two lines intersect, they are perpendicular.

5. p q Logic p: The person is a senior. q: The person is mature. If the person is a senior then the person is mature. If p, then q

6. Logic Let p: I get a job. Let q: I will earn money. Let r: I will go to the movies. Let s: I will spend my money. Translate to English 1. If p then q. 2. If q then r. 3. If p then r. 4. If r then s.

7. 2. Logic Let p: Today is Wednesday. Let q: Tomorrow is Thursday. Let r: Friday is coming. Let s: Yesterday was Tuesday. Translate to logic statements. 5. If today is Wednesday, then tomorrow is Thursday. 6. If tomorrow is Thursday, then Friday is coming. 7. If yesterday was Tuesday, then tomorrow is Thursday. 8. If yesterday was Tuesday, then Friday is coming.

8. Let’s look at some more examples…

9. Truth Table for Conditionals • The only time you can say a conditional is false is when the hypothesis is true and conclusion is false.

10. Related Conditionals • Converse: exchanging the hypothesis and conclusion of the conditional. • Inverse: negating both the hypothesis and conclusion of the conditional. • Contrapositive: negating both the hypothesis and conclusion of the converse statement. • Look at the conditional: If it is nice outside, we will have softball practice.

11. Interesting Notes • If a conditional is true, its contrapositive is always true. • If a conditional is false, its contrapositive is always false. • The converse and inverse are either both true or both false. • Logically equivalent statements are statements with the same truth values. • Conditional and Contrapositive • Inverse and Converse

12. Alice in Wonderland

13. Chapter 2 Section 4 Deductive Reasoning

14. What is deductive reasoning? • Deductive reasoning uses facts, rules, definitions, or properties to reach logical conclusions.

15. Law of Detachment • If p q is true and p is true, then q is also true. • Basically, you can determine that if the conditional is true and p is true, q is true.

16. If you are a freshman, you are young. Mark is a freshman. Mark is young.

17. If you are a freshman, then you are young. Mark is not a freshman. Mark is not young.

18. If you are a freshman, then you are young. • Jim is young. • According to the Law of Detachment, can you say that Jim is a freshman?

19. All boys like cars. Mark is a boy . Mark likes cars.

20. Law of Syllogism • The law of syllogism is similar to the Transitive Property of Equality. • If p q and q r are true, then p r is also true.

21. If it rains, we will stay inside. • If we stay inside, we will play checkers. • If it rains, we will play checkers.

22. If WV wins, we will have a party. • If WV wins, I will cry with joy. • If we have a party, I will cry with joy. FALSE

23. If my dog dies, I am sad. • If I am sad, my mom will buy me a puppy. • If my mom buys me a puppy, I will be happy. • If my dog dies, I will be happy.