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necessary and sufficient conditions


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Conditions which must be satisfied for something to be true (necessary) and if satisfied imply that it must occur (sufficient). Consider propositions B and C. ‘B is a sufficient condition for C’ means that if B is true, C is always true. ‘B is a necessary condition for C’ means that C cannot be true unless B is true. A condition can be sufficient but not necessary; if B is a sufficient condition for C, C cannot be false when B is true, but C could well be true when B is false. It is possible for the same condition to be both necessary and sufficient; this means that B is true if and only if (written iff) C is true. Thus if B is a necessary and sufficient condition for C, C must likewise be a necessary and sufficient condition for B; the two statements are thus equivalent.

Subjects: Economics.


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