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.
Related category LOGIC
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