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Logical biconditional

In logical calculus of mathematics, logical biconditional is a logical operator connecting two statements to assert, p if and only if q where p is a hypothesis (or antecedent) and q is a conclusion (or consequent). The operator is denoted using a doubleheaded arrow "↔". It is logically equivalent to (p→q)(q→p).

The hypothesis is sometimes also called "necessary condition" while the conclusion may be called "sufficient condition".

It is defined using the following truth table:

p q | p ↔ q

+-------- T T | T T F | F F T | F F F | T

The only difference from logical conditional is the case when the hypothesis is false but the conclusion is true. In that case, in conditional, the result is true, yet in biconditional the result is false.