Sufficient condition

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A sufficient condition is one for which the following is true:

If A is a sufficient condition of B, then if A is true, B must be true.

For example, "I heard thunder" is a sufficient condition of "There was lightning nearby," because if I heard thunder, there must have been lightning nearby to cause it. However, "There was lightning nearby" is not a sufficient cause of "I heard thunder," because there may have been lightning nearby that I did not hear.

Confusing a sufficient condition with a necessary and sufficient condition is a logical fallacy known as affirming the consequent.

From the affirmation of a sufficient condition, one may infer that the necessary condition is true.

See also

Modus ponens

Modus tollens