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A condition can be both necessary and sufficient. For example, at present, "today is the Fourth of July" is a necessary and sufficient condition for "today is Independence Day in the United States". Similarly, a necessary and sufficient condition for invertibility of a matrix M is that M has a nonzero determinant.
A necessary cause is one without which it would be impossible for an effect to occur, while a sufficient cause is one whose presence guarantees the occurrence of an effect. These concepts are largely based on but distinct from ideas of necessity and sufficiency in logic .
In writing, phrases commonly used as alternatives to P "if and only if" Q include: Q is necessary and sufficient for P, for P it is necessary and sufficient that Q, P is equivalent (or materially equivalent) to Q (compare with material implication), P precisely if Q, P precisely (or exactly) when Q, P exactly in case Q, and P just in case Q. [3]
That is, necessary truths depend upon the principle of contradiction." [11] The sufficient reason for a necessary truth is that its negation is a contradiction. [4] Leibniz admitted contingent truths, that is, facts in the world that are not necessarily true, but that are nonetheless true.
Causes may sometimes be distinguished into two types: necessary and sufficient. [19] A third type of causation, which requires neither necessity nor sufficiency, but which contributes to the effect, is called a "contributory cause". Necessary causes If x is a necessary cause of y, then the presence of y necessarily implies the prior occurrence ...
Liability coverage is the backbone of your policy and is required by law in most states — except in New Hampshire, which may make an exception if you can prove that you have sufficient assets to ...
Getting five to 30 minutes of UV exposure midday at least a few times a week is thought to be enough to maintain sufficient vitamin D levels, per the NIH. ... year-round and may be necessary ...
One player isn’t sufficient to fuel a team’s playoff berth and deep postseason run. But one player is also necessary to chase such goals: a strong quarterback. And the Commanders have him.