Necessity and sufficiency

In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is "necessarily" guaranteed by the truth of P. (Equivalently, it is impossible to have P without Q, or the falsity of Q ensures the falsity of P.) Similarly, P is sufficient for Q, because P being true always or "sufficiently" implies that Q is true, but P not being true does not always imply that Q is not true.

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