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Necessary and sufficient condition
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This article is about the formal terminology in logic. For causal meanings of the terms, see

Causality.
In

logic, the words necessity and sufficiency refer to the implicational relationships between

statements. The assertion that one statement is a necessary and sufficient condition of another means that the former statement is true

if and only if the latter is true.

## Contents

## Definitions

A necessary condition of a statement must be satisfied for the statement to be true. Formally, a statement P is a necessary condition of a statement Q if Q implies P (Q P).
A sufficient condition is one that, if satisfied, assures the statement's truth. Formally, a statement P is a sufficient condition of a statement Q if P implies Q (P Q).

## Necessary conditions

The sun being above the horizon is a necessary condition for direct sunlight; but it is not a sufficient condition as something else may be casting a shadow, e.g. in the case of an

eclipse.
The assertion that P is necessary for Q is colloquially equivalent to "Q cannot be true unless P is true," or "if P is false th...

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