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necessity and sufficiency

In mathematical analysis, conditions which describe the validity of a statement.For example, in the case of 4 < a < 10 it is necessary that, say, 3 < a < 11 since if this were not true then the original statement would not be true; and sufficient that 5 < a < 9, since is this is true it implies the truth of the original statement. More generally, in logic, a condition is necessary for the truth of a statement if the falsehood of the condition implies the falsehood of the statement, and sufficient if the truth of the condition implies the truth of the statement. See also necessity.

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   • LOGIC