TeXipedia

veebar

Represents the logical XOR (exclusive or) operation, commonly used in mathematical logic and set theory.

Overview

Serves as a fundamental operator in propositional logic and Boolean algebra, indicating that exactly one of two propositions is true but not both.

  • Essential in digital circuit design and computer science for expressing exclusive conditions
  • Used in formal proofs and mathematical reasoning
  • Appears in set theory to denote symmetric difference between sets
  • Common in academic papers and technical documentation where precise logical relationships need to be expressed

Examples

Logical XOR (exclusive or) operation in mathematical logic.

pq    (pq)¬(pq)p \veebar q \iff (p \lor q) \land \neg(p \land q)
p \veebar q \iff (p \lor q) \land \neg(p \land q)

Set theory operation showing symmetric difference of sets.

AB=(AB)(BA)A \veebar B = (A \setminus B) \cup (B \setminus A)
A \veebar B = (A \setminus B) \cup (B \setminus A)

Boolean algebra expression with multiple variables.

xyz=(xy)zx \veebar y \veebar z = (x \oplus y) \oplus z
x \veebar y \veebar z = (x \oplus y) \oplus z