1. CONDITIONALS

2. Conditional Statement: Any statement that is or can be written in if- then form. That is, If p then q.

3. Symbolically we use the following for the conditional statement: “If p then q”:

4. Hypothesis: The “condition” that has to be met. It is the p statement that follows the word if in a conditional statement.

5. Conclusion: The result or consequence. The q statement that follows the then in a conditional statement.

6. EXAMPLE: If you feed the dog, then you may go to the movies.

7. EXAMPLE: If you feed the dog, then you may go to the movies. Hypothesis

8. EXAMPLE: If you feed the dog, then you may go to the movies. Hypothesis Conclusion

9. EXAMPLE: The game will be cancelled if it rains.

10. EXAMPLE: The game will be cancelled if it rains. Hypothesis

11. EXAMPLE: The game will be cancelled if it rains. Hypothesis Conclusion

12. Note: The hypothesis does not always appear first in a statement.

13. “ALL” Statements: When changing an “all” statement to if-then form, the hypothesis must be made singular.

14. EXAMPLE: All rectangles have four sides. BECOMES: If _______ a rectangle then _____ four sides. a figure is it has

15. RELATED CONDITIONALS

16. The Converse: The conditional statement formed by interchanging the hypothesis and conclusion.

17. Symbolically, for the conditional statement: The converse is:

18. EXAMPLE: Form the converse of: IfthenX=2X > 0.

19. EXAMPLE: Form the converse of: IfthenX=2X > 0. IfthenX > 0X=2.

20. The Inverse: The conditional statement formed by negating both the hypothesis and conclusion.

21. Symbolically, for the conditional statement: The inverse is:

22. EXAMPLE: Form the Inverse of: IfthenX=2X > 0. IfthenX=2X > 0.

23. EXAMPLE: Form the Inverse of: IfthenX=2X > 0. IfthenX=2X > 0.

24. The Contrapositive: The conditional statement formed by interchanging and negating the hypothesis and conclusion.

25. Symbolically, for the conditional statement: The contrapositive is:

26. EXAMPLE: Form the contrapositive of: IfthenX=2X > 0. IfthenX=2X > 0.

27. Note: Any statement and its Contrapositive have the same truth value.

28. LET’S PRACTICE !

29. GIVEN: If x is 5 then x is odd. What form is: If x is odd then x is 5. ? CONVERSE

30. GIVEN: If x is 5 then x is odd. What form is: If x is not odd then x is not 5. ? CONTRAPOSITIVE

31. GIVEN: If x is 5 then x is odd. What form is: If x is not 5 then x is not odd. ? INVERSE

32. GIVEN: If x is odd then x is 5. What form is: If x is 5 then x is odd.? CONVERSE

33. THE END !!