Exclusive disjunction

Exclusive disjunction

Exclusive disjunction (often abbreviated as XOR) is the logical operation that returns true if exactly one of the propositions is true, but not both.

Symbols

• p ⊕ q (standard notation)
• p XOR q (common in computer science)
• (p ∨ q) ∧ ¬(p ∧ q) (definition using basic operators)

Definition

The exclusive disjunction p ⊕ q is true if either p or q is true, but false if both are true or both are false.

Truth Table

p	q	p ⊕ q
T	T	F
T	F	T
F	T	T
F	F	F

Examples

• If p = "I go jogging" and q = "I go swimming",

 then p ⊕ q = "I go jogging or swimming, but not both".

• In Python: p ^ q (when p and q are booleans)
• In Java: p ^ q (when p and q are booleans)