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Represents the logical AND operator in mathematical logic and set theory, indicating conjunction between two propositions.

Overview

Essential in formal logic, mathematical proofs, and computer science for expressing compound logical statements where both conditions must be true.

  • Commonly used in truth tables and logical expressions
  • Appears frequently in discrete mathematics and boolean algebra
  • Alternative to using "∧" in typeset mathematics
  • Particularly useful when writing formal proofs or defining logical conditions in theoretical computer science

Examples

Logical AND operation in a boolean expression

p∧q  ⟹  rp \land q \implies r 
p \land q \implies r

Compound logical statement with multiple AND operations

(A∧B)∧(C∧D)(A \land B) \land (C \land D) 
(A \land B) \land (C \land D)

Set intersection expressed using logical AND

x∈A∧x∈B  ⟺  x∈(A∩B)x \in A \land x \in B \iff x \in (A \cap B) 
x \in A \land x \in B \iff x \in (A \cap B)