Friday, 15 November 2019

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

Laws of Set Operations Class 11 Maths - Sets

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

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:

No comments:

Post a comment

We love to hear your thoughts about this post!