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 /nonoccurrence) [as the case may be]
of A guarantees (or brings about) the falsity (/nonexistence
/nonoccurrence) 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).
 x's being a square is a sufficient condition for x's being a rectangle.
 x's being a square is a necessary condition for x's being a rectangle.
 x's being a rectangle is a sufficient condition for x's being a square.
 x's being a rectangle is a necessary condition for x's being a square.
 x's being a mother is a sufficient condition for x's being a female.
 x's being a mother is a necessary condition for x's being a female.
 x's being a female is a sufficient condition for x's being a mother.
 x's being a female is a necessary condition for x's being a mother.
 x's being greater than 15 is a sufficient condition for x's being less than 20.
 x's being greater than 15 is a necessary condition for x's being less than 20.
 x's being less than 20 is a sufficient condition for x's being greater than 15.
 x's being less than 20 is a necessary condition for x's being greater than 15.
 x's being less than 12 is a sufficient condition for x's being less than 20.
 x's being less than 12 is a necessary condition for x's being less than 20.
 x's being less than 20 is a sufficient condition for x's being less than 12.
 x's being less than 20 is a necessary condition for x's being less than 12.
 x's having two arms is a sufficient condition for x's being a human being.
 x's having two arms is a necessary condition for x's being a human being.
 x's wanting to do a is a sufficient condition for x's doing a.
 x's wanting to do a is a necessary condition for x's doing a.
 x's being an equilateral rectangle is a sufficient condition for x's being a square.
 x's being an equilateral rectangle is a necessary condition for x's being a square.

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