Solved Paper-II On Topic : Solved Paper-II December 2004

Que : 1 . AVA = A is called: 1 Identity law 2 De Morgan’s law 3 Idempotent law 4 Complement law
Please Select Ans Options .
Explanation

Option 3 is Correct Answer
1. Commutative Laws:
For any two finite sets A and B;
(i) A U B = B U A
(ii) A ∩ B = B ∩ A
2. Associative Laws:
For any three finite sets A, B and C;
(i) (A U B) U C = A U (B U C)
(ii) (A ∩ B) ∩ C = A ∩ (B ∩ C)
Thus, union and intersection are associative.
3. Idempotent Laws:
For any finite set A;
(i) A U A = A
(ii) A ∩ A = A
4. Distributive Laws:
For any three finite sets A, B and C;
(i) A U (B ∩ C) = (A U B) ∩ (A U C)
(ii) A ∩ (B U C) = (A ∩ B) U (A ∩ C)
Thus, union and intersection are distributive over intersection and union respectively.
5. De Morgan’s Laws:
For any two finite sets A and B;
(i) A – (B U C) = (A – B) ∩ (A – C)
(ii) A – (B ∩ C) = (A – B) U (A – C)
De Morgan’s Laws can also we written as:
(i) (A U B)’ = A’ ∩ B’
(ii) (A ∩ B)’ = A’ U B’
More laws of algebra of sets:
6. For any two finite sets A and B;
(i) A – B = A ∩ B’
(ii) B – A = B ∩ A’
(iii) A – B = A ⇔ A ∩ B = ∅