TeXipedia

lor

Represents the logical OR operator in mathematical logic and set theory, indicating that at least one of two conditions is true.

Overview

Essential in formal logic, boolean algebra, and computer science for expressing disjunction between propositions or conditions.

  • Commonly used in truth tables and logical proofs
  • Appears frequently in set theory when describing unions
  • Important in digital circuit design and programming logic
  • Often paired with other logical operators like AND (\land) and NOT (\neg) to build complex logical expressions

Examples

Basic logical OR operation between two propositions P and Q.

P∨QP \lor Q 
P \lor Q

Complex logical expression combining multiple OR operations.

(A∨B)∨(C∨D)(A \lor B) \lor (C \lor D) 
(A \lor B) \lor (C \lor D)

Truth condition in set theory using logical OR.

x∈A∨x∈Bx \in A \lor x \in B 
x \in A \lor x \in B