Intersection (set theory)

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Definition

If and only if Prime numbers Odd numbers Singleton set Inhabited set

8 related topics

Algebraic properties

Associative Commutative Idempotent Logical conjunction Distributes

8 related topics

Nullary intersection

Set-builder notation Vacuous truth Universal set Identity element ZF

6 related topics

Arbitrary intersections

For every Index set Natural numbers Infinite product Σ-algebras

5 related topics

Key facts & relationships

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Field: Set theory
Statement: The intersection of A {\displaystyle A} and B {\displaystyle B} is the set A ∩ B {\displaystyle A\cap B} of elements that lie in both set A {\displaystyle A} and set B {\display…
Symbolic statement: A ∩ B = { x : x ∈ A and x ∈ B } {\displaystyle A\cap B=\{x:x\in A{\text{ and }}x\in B\}}
Type: Set operation

Topics to explore

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Overview

Set theory
Sets Set (mathematics)
Algebraic operation
With sets as operands Set operation (Boolean)
Geometry
Encountered Intersection (geometry)
Points Point (geometry)
Uncountable sets Uncountable set

Notation and terminology

Definition

If and only if
Prime numbers Prime number
Odd numbers
Singleton set
Inhabited set
Disjoint Disjoint sets
Empty Empty set
Multiples Multiple (mathematics)

Algebraic properties

Associative
Commutative Commutative property
Idempotent Idempotence
Logical conjunction
Distributes Distributive property
Union Union (set theory)
Complement Complement (set theory)
De Morgan's laws

Arbitrary intersections

For every Universal quantification
Index set
Natural numbers Natural number
Infinite product
Σ-algebras Sigma algebra

Nullary intersection

Advanced semantic analysis

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Map overview Semantic statistics

Nodes45

Edges44

Triples6

Avg. degree1.96

Density0.044444

Components1

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Intersection (set theory)

Top relations

Field · 1

Intersection (set theory) → Set theory

Statement · 1

Intersection (set theory) → The intersection of A {\displaystyle A} and B {\displaystyle B} is the set A ∩ B {\displaystyle A\cap B} of elements that lie in both set A {\displaystyle A} and set B {\display…

Symbolic statement · 1

Intersection (set theory) → A ∩ B = { x : x ∈ A and x ∈ B } {\displaystyle A\cap B=\{x:x\in A{\text{ and }}x\in B\}}

Type · 1

Intersection (set theory) → Set operation

Important terminology Word statistics

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Important terminology

displaystyle intersection set sets cap empty bigcap also theory two elements notation case disjoint operation varnothing collection written example one

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Intersection (set theory)	Field	Set theory	1.00	infobox
Intersection (set theory)	Statement	The intersection of A {\displaystyle A} and B {\displaystyle B} is the set A ∩ B {\displaystyle A\cap B} of elements that lie in both set A {\displaystyle A} and set B {\display…	1.00	infobox
Intersection (set theory)	Symbolic statement	A ∩ B = { x : x ∈ A and x ∈ B } {\displaystyle A\cap B=\{x:x\in A{\text{ and }}x\in B\}}	1.00	infobox
Intersection (set theory)	Type	Set operation	1.00	infobox
two lines is a singleton set of one point for distinct non-parallel lines in the same plane.Intersecting	instance of	because 9 is not prime.The intersection of two geometric sets of points	0.80	text
disjoint setsWe say that .mw-parser-output .vanchor	instance of	because 9 is not prime.The intersection of two geometric sets of points	0.80	text

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Min side: 3