CBSE Class 11 Maths - Laws of Set Operations (#class11Maths)(#eduvictors)

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)

☛See Also:

 Special Mathematical Constants

 SETS (NCERT Ex 1.1)
 SETS (NCERT Ex 1.2)
 Different Types of Sets
 SETS (NCERT Ex 1.3)

 SETS (Unit Test Paper)
SETS (VENN DIAGRAMS)
SETS (Operations of Sets)
SETS (NCERT Ex 1.4 Q1-Q5)
SETS (NCERT Ex 1.4 Q6 - Q8)