Math Formulas ► Complex numbers ► Sets of Numbers ► Set Identities
Math Formulas ► Set Identities
Definitions:
Universal set : I
Empty set: ∅
Union of sets
A∪B={x:x∈A or x∈B}
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Intersection of sets
A∩B={x:x∈A and x∈B}
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Complement
A′={x∈I:x/∈A}
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Difference of sets
A∖B={x:x∈A and x/∈B}
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Cartesian product
A×B={(x,y):x∈A and y∈B}
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Set identities involving union
Commutativity
A∪B=B∪A
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Associativity
A∪(B∪C)=(A∪B)∪C
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Idempotency
A∪A=A
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Set identities involving intersection
Commutativity
A∩B=B∩A
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Associativity
A∩(B∩C)=(A∩B)∩C
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Idempotency
A∩A=A
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Set identities involving union and intersection
Distributivity
A∪(B∩C)=(A∪B)∩(A∪C)
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A∩(B∪C)=(A∩B)∪(A∩C)
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Domination
A∩∅=∅
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A∪I=I
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Identity
A∪∅=∅
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A∩I=A
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Set identities involving union, intersection and complement
Complement of intersection and union
A∪A′=I
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A∩A′=∅
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De Morgan's laws
(A∪B)′=A′∩B ′
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(A∩B)′=A′∪B ′
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Set identities involving difference
B∖A=B∖(A∪B)
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B∖A=B∩A′
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A∖A=∅
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(A∖B)∩C=(A∩C)∖(B∩C)
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A′=I∖A
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