Exclusive Disjunction

Exclusive Disjunction

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.

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