Question

All identities of sets​

Answer 1

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Note that in these examples, A, B and C are sets, and U denotes the universal set — that is, the set containing all elements in the domain. ∅ denotes the empty set. Note also that, in these examples, an absolute complement is written AC. It may also be written as A, A′ or ∁(A) in different sources.

Identity Laws

A ∪ ∅ = A

A ∩ U = A

Domination Laws

A ∪ U = U

A ∩ ∅ = ∅

Complement Laws

A ∪ AC = U

A ∩ AC = ∅

Idempotent Laws

A ∪ A = A

A ∩ A = A

Involution or Double Complement Law

(AC)C = A

Absorption Laws

A ∪ (A ∩ B) = A

A ∩ (A ∪ B) = A

Associative Laws

A ∪ (B ∪ C) = (A ∪ B) ∪ C

A ∩ (B ∩ C) = (A ∩ B) ∩ C

Communative Laws

A ∪ B = B ∪ A

A ∩ B = B ∩ A

Distributive Laws

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

De Morgan’s Laws

(A ∪ B)C = AC ∩ BC

(A ∩ B)C = AC ∪ BC

Note: The term ‘De Morgan’s Laws’ also refers to rules of inference in logic.

Set Complement Laws

A - B = A ∩ BC

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Answer 2

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