Conditional Statements

1. ConditionalStatements

2. Conditional Statement An “if” … “then” …. (may be true or false) Example: If you eat Doritos, then you will have bad breath.

3. Conditional Statement If p, then q.

4. Hypothesis The part of a conditional statement after the “if” If you stick your finger in the electrical socket, then I will laugh. If you stick your finger in the electrical socket, then I will laugh.

5. Conclusion The part of a conditional statement after the “then” If you stick your finger in the electrical socket, then I will laugh. If you stick your finger in the electrical socket, then I will laugh.

6. Converse When you switch the hypothesis and conclusion of a conditional statement. (The “If” and “then” do not move) Conditional: If you stick your finger in the electrical socket, then I will laugh. If you stick your finger in the electrical socket, then I will laugh. Converse: If I laugh, then you stuck your finger in the electrical socket.

7. Converse When you switch the hypothesis and conclusion of a conditional statement. (The “If” and “then” do not move) Conditional: If p, then q. Converse: If q, then p.

8. Write the converse of the following statement. Conditional: If you eat Doritos, then you have bad breath. If you eat Doritos, then you have bad breath. Converse: If you have bad breath, then you ate Doritos.

9. Inverse When you negate the hypothesis and conclusion of a conditional statement. Conditional: If you stick your finger in the electrical socket, then I will laugh. If you stick your finger in the electrical socket, then I will laugh. Inverse: If you do not stick your finger in the electrical socket, then I will not laugh.

10. Inverse When you negate the hypothesis and conclusion of a conditional statement. Conditional: If p, then q. Inverse: If ~p, then ~q.

11. Write the inverse of the following statement. Conditional: If you shave your head, then you will look like Britney Spears. If you shave your head, then you will look like Britney Spears. Inverse: If you do not shave your head, then you will not look like Britney Spears.

12. Contrapositive When you switch AND negate the hypothesis and conclusion of a conditional statement. (The “If” and “then” do not move) Conditional: If you stick your finger in the electrical socket, then I will laugh. If you stick your finger in the electrical socket, then I will laugh. Contrapositive: If I do not laugh, then you did not stick your finger in the electrical socket.

13. Contrapositive When you switch AND negate the hypothesis and conclusion of a conditional statement. (The “If” and “then” do not move) Conditional: If p, then q. Contrapositive: If ~q, then ~p.

14. Write the contrapositive of the following statement. Conditional: If you like enchiladas, then we can be best friends. If you like enchiladas, then we can be best friends. Contrapositive: If we are not best friends, then you do not like enchiladas.

15. False Statement Any statement that can be disproved. All red heads are un-athletic. False.

16. Counterexample An example that disproves a false statement. Example:All red heads are un-athletic. False. Counterexample: Shaun White Andy Dalton Blake Griffin

17. Rewrite the statement into a conditional statement then determine if the following is true or false; if false, give a counterexample. All squares are rectangles. Conditional Statement: If it is a square, then it is a rectangle. True or False: True.

18. Rewrite the statement into a conditional statement then determine if the following is true or false; if false, give a counterexample. All rectangles are squares. Conditional Statement: If it is a rectangle, then it is a square. True or False: False. Counterexample: Not all rectangles have side lengths thatare the same.

19. Law of Syllogism If a=b and b=c then a = c

20. Law of Syllogism Marsha is older than Jan. Jan is older than Cindy. Then Marsha is older than Cindy.

21. Law of Syllogism Mrs. Wenter is a nerd. All nerds love math. then Mrs. Wenter loves math.