Department of Philosophy
Simon Fraser University

First Set of Practice Exercises on
Necessary Conditions and Sufficient Conditions

Definition of "Sufficient condition"

 Definition: A condition A is said to be sufficient for a condition B, if (and only if) the truth (/existence /occurrence) [as the case may be] of A guarantees (or brings about) the truth (/existence /occurrence) of B.

Definition of "Necessary condition"

 Definition: A condition A is said to be necessary for a condition B, if (and only if) the falsity (/nonexistence /non-occurrence) [as the case may be] of A guarantees (or brings about) the falsity (/nonexistence /non-occurrence) of B.

For each of the following, say whether it is true or false. For the answers, click on "Answers" at the bottom of this page (after question #22).
1. x's being a square is a sufficient condition for x's being a rectangle.

2. x's being a square is a necessary condition for x's being a rectangle.

3. x's being a rectangle is a sufficient condition for x's being a square.

4. x's being a rectangle is a necessary condition for x's being a square.

5. x's being a mother is a sufficient condition for x's being a female.

6. x's being a mother is a necessary condition for x's being a female.

7. x's being a female is a sufficient condition for x's being a mother.

8. x's being a female is a necessary condition for x's being a mother.

9. x's being greater than 15 is a sufficient condition for x's being less than 20.

10. x's being greater than 15 is a necessary condition for x's being less than 20.

11. x's being less than 20 is a sufficient condition for x's being greater than 15.

12. x's being less than 20 is a necessary condition for x's being greater than 15.

13. x's being less than 12 is a sufficient condition for x's being less than 20.

14. x's being less than 12 is a necessary condition for x's being less than 20.

15. x's being less than 20 is a sufficient condition for x's being less than 12.

16. x's being less than 20 is a necessary condition for x's being less than 12.

17. x's having two arms is a sufficient condition for x's being a human being.

18. x's having two arms is a necessary condition for x's being a human being.

19. x's wanting to do a is a sufficient condition for x's doing a.

20. x's wanting to do a is a necessary condition for x's doing a.

21. x's being an equilateral rectangle is a sufficient condition for x's being a square.

22. x's being an equilateral rectangle is a necessary condition for x's being a square.