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:

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.