MATH 125 6.2 Set Identities

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Last updated 6:07 PM on 3/27/25
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12 Terms

1
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Commutative laws

A ∩ B = B ∩ A

A ∪ B = B ∪ A

2
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Associative laws

(A ∩ B) ∩ C = A ∩ (B ∩ C)

(A ∪ B) ∪ C = A ∪ (B ∪ C)

3
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Distributive laws

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

4
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Identity laws

A ∩ U = A

A ∪ ∅ = A

5
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Complement laws

A ∪ A’ = U

A ∩ A’ = ∅

6
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Double complement law

(A’)’ = A

7
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Idempotent law

A ∩ A = A

A ∪ A = A

8
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Universal bound law

A ∩ ∅ = ∅

A ∪ U = U

9
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De Morgan’s laws

(A ∩ B)’ = A’ ∪ B’

(A ∪ B)’ = A’ ∩ B’

10
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Absorption law

A ∩ (A ∪ B) = A

A ∪ (A ∩ B) = A

11
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Complements of U and ∅

U’ = ∅

∅’ = U

12
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Set difference law

A - B = A ∩ B’