Discrete Set Operations Identities

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discrete

discrete math

set operations

set identities

identities

math

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10 Terms

1
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Identity laws

A∩U = A

A∪∅=A

2
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Domination laws

A∪U=U

A∩∅=∅

3
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Idempotent laws

A∪A=A

A∩A=A

4
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Complementation law

bar(A-bar) = A

5
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Commutative laws

A∪B = B∪A

A∩B = B∩A

6
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Associative laws

A∪(B∪C) = (A∪B)∪C

A∩(B∩C) = (A∩B)∩C

7
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Distributive laws

A∪(B∩C) = (A∪B)∩(A∪C)

A∩(B∪C) = (A∩B)∪(A∩C)

8
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De Morgan’s laws

bar(A∩B) = A-bar ∪ B-bar

bar(A∪B) = A-bar ∩ B-bar

9
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Absorption laws

A∪(A∩B) = A

A∩(A∪B) = A

10
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Complement laws

A∪A-bar = U

A∩A-bar = ∅