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.