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" 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 |    T
F F |    T

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.