Mastering Set Notations and DeMorgan’s Law: A Comprehensive Guide

Mastering Set Notations and DeMorgan’s Law: A Comprehensive Guide

The commutative laws

A ∪ B = B ∪ A

A ∩ B = B ∩ A

Associative laws

(A ∪ B) ∪ C = A ∪ (B ∪ C)

(A ∩ B) ∩ C = A ∩ (B ∩ C)

Distributive laws

A ∩ (B ∪ C) = (A ∩ B)U (A ∩ C)

A U (B ∩ C ) = (A ∪ B) ∩ (A ∪ C)

Idempotent laws

A U A = A

A ∩ A = A

Identity laws

A ∪ ∅ = A

A ∩ U = A

Universal Bound laws

A ∪ U= U

A ∪ ∅ = ∅

DeMorgan’s law

(A ∪ B)c = Ac ∩ Bc

(A ∩ B)c = Ac ∪ Bc

Complement laws

A ∪ Ac = U

(A ∩ A)c = ∅

complement of U and ∅

Uc = ∅

c= ∪

Double Complement law

(Ac)c =A

Set Difference law

A – B = A ∩ Bc


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