Intersection symbol (∩)
∩ means “intersection”: A ∩ B is the set of the elements that are in both A and B. It is read “A intersection B”, and sometimes “A cap B”.
Easily confused with
How to read it
OpenStax’s Contemporary Mathematics defines A ∩ B as {x | x ∈ A and x ∈ B}, the members the two sets share, and calls intersection a logical AND. Oscar Levin’s Discrete Mathematics gives the example {1, 2, 3} ∩ {2, 3, 4} = {2, 3}. Two sets with nothing in common, such as the even and the odd digits, are disjoint, and their intersection is the empty set ∅ (OpenStax). Unicode names the character INTERSECTION (U+2229), also called cap or hat, and has an n-ary form ⋂ (U+22C2) for the intersection of many sets. NIST’s Digital Library of Mathematical Functions lists it in its common notations.
Also searched as: ∩, A ∩ B, cap symbol, intersection of sets, upside down u symbol.
∩ and ∧
The intersection is the set version of ∧, the logical “and”: x is in A ∩ B when x ∈ A ∧ x ∈ B. The Union symbol (∪) ∪ is the same shape the other way up and means “or”.
Read next
- Next in Set theory symbolsComplement of a set (A′)A′, read “A prime”, is the complement of the set A: everything in the universal set that is not in A. Other books write it Aᶜ or Ā.
- In Logic symbolsAnd symbol (∧)∧ means “and” in logic. p ∧ q, read “p and q”, is a conjunction: it is true only when both p and q are true.
More set theory symbols
The same shape elsewhere
Browse symbols drawn with curves and waves.
Sources
- Contemporary Mathematics, 1.4 Set Operations with Two Sets, OpenStax (Rice University), Intersection of two sets
- Discrete Mathematics, 0.3 Sets, Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd edition, Oscar Levin, University of Northern Colorado (Open Math Books), Set theory notation
- Earliest Uses of Symbols of Set Theory and Logic, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Intersection and union
- NIST Digital Library of Mathematical Functions: Introduction (Common Notations and Definitions), U.S. National Institute of Standards and Technology, Common Notations and Definitions
- Mathematical Operators: Range 2200–22FF (code chart), The Unicode Standard, Version 18.0, Unicode Consortium, Logical and set operators, 2229
Researched, edited and approved by Rory Hansen before publishing. Last reviewed October 9, 2026. How we research
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