The exclusive disjunction of the propositions P and Q is the proposition that corresponds to (P ∨ Q) ∧ ¬(P ∧ Q), which means that it is true when one or the other of the propositions P and Q is true, but not both at the same time.

### Symbol

The exclusive disjunction of the propositions P and Q is noted as “P ∨ Q” and is read as “P or Q but not P and Q”.

### Property

The truth table of an exclusive disjunction is:

P |
Q |
P ∨ Q |

1 | 1 | 0 |

1 | 0 | 1 |

0 | 1 | 1 |

0 | 0 | 0 |

in which 1 = true and 0 = false.