| 单词 | necessary and sufficient conditions |
| 释义 | necessary and sufficient conditions Logical relations between two statements. 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. 'B is a sufficient condition for C' thus implies 'c is a necessary condition for B'. 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. Equally, a condition can be necessary but not sufficient; if B is a necessary condition for C, C cannot be true if B is false, but C could well be false when B is true. It is however 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. |
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