## Laws of Set Operations Class 11 Maths - Sets

Sets under the operations of union, intersection and complement satisfy various laws. These laws collectively called Algebra of sets.

Here follows few important Laws of Set Operations

1. Idempotent Laws:
(a) A ∪ A = A
(b) A ∩ A = A

2. Commutative Laws:
(a) A ∪ B = B ∪ A
(b) A ∩ B = B ∩ A

3. Associative Laws:
(a) (A ∪ B) ∪ C = A ∪ (B ∪ C)
(b) (A ∩ B) ∩ C = A ∩ (B ∩ C)

4. Identity Laws:
(a) A ∪ φ = A
(b) A ∩ φ = φ
(c) A ∪ U = U
(d) A ∩ U = A

5. Distributive Laws:
(a) A ∪ (B ∩ C ) = (A ∪ B) ∩ (A ∪ C)
(b) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

6. Involution Laws:
(a) (A')'  = A [A' = complement of set A]

7. Complement Laws:
(a) A ∪ A' = U
(b) A ∩ A' = φ
(c) U' = φ
(d) φ'  = U

8. De Morgan's Laws:
(a) (A ∪ B)' = A' ∩ B'
(b) (A ∩ B)' = A' ∪ B'

9. For any three sets A, B and C
(a) A - (B ∪ C ) = (A - B) ∩ (A - C)
(b) A - (B ∩ C)  = (A - B) ∪ (A - C)

10. Cardinal property of Sets
(a) n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
(b) if A and B are disjoint sets then n(A ∪ B) = n(A) + n(B)  