Copyright © 1997, Norman Swartz
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.

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