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Logical conditional

In logical calculus of mathematics, logical conditional is a binary logical operator connecting two statements, if p then q where p is a hypothesis (or antecedent) and q is a conclusion (or consequent). The operator is denoted using an left-arrow "→".

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

It is defined using the following truth table:
pqp → q

In the case that the hypothesis is true, the result is the same as conclusion. Otherwise, the whole statement is true regardless the value of conclusion.