The implication of Q by P is the proposition (¬P) ∨ Q, noted as “P ⇒ Q” or “P

*implies*Q” which is false only if the proposition P is true and the proposition Q is false. The implication is true in all other cases.### Symbol

The symbol of a logical implication is “P ⇒ Q” which is read as “P implies Q”.

In other words, P ⇒ Q means that the conditional P → Q is always true.

### Property

The truth table of a logical implication is:

P |
Q |
P ⇒ Q |

1 | 1 | 1 |

1 | 0 | 0 |

0 | 1 | 1 |

0 | 0 | 1 |

In which 1 = true and 0 = false.