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# Conditional (if-then)

_{ Jan 01 . 2001 }

Any two propositions **P** and **Q** can be joined by a conditional operator, producing the new, complex, proposition:

**If P then Q**

The proposition **If P then Q** is true if and only if either **P** is false or **Q** is true. It is false only when **P** is true and **Q** is false.

## Truth Table

P | Q | If P then Q |

T | T | T |

T | F | F |

F | T | T |

F | F | T |

## Commentary

A special conditional occurs if we flip the

PandQaround: we getif Q then P, which is the same as sayingP only if Q.