

InterviewSolution
Saved Bookmarks
1. |
Consider the following for any three non empty sets A, B and C.1. A – (B ∪ C) = (A – B) ∪ (A – C) 2. A – B = A – (A ∩ B) 3. A = (A ∩ B) ∪ (A – B) which of the above is /are correct? (a) Only 1 (b) 2 and 3 (c) 1 and 2 (d) 1 and 3 |
Answer» (b) 2 and 3 1. A – (B ∪ C) = (A – B) ∪ (A – C) (A – B) ∪ (A – C) ⇒ For all (x ∈ A and x ∉ B) or (x ∈ A and x ∉ C) ⇒ For all (x ∈ A and x ∉ B and x ∉ C) ⇒ x ∈ A – (B ∩ C ) Hence not correct. 2. x ∈ (A – (A ∩ B)) ⇒ x ∈ A and x ∉ A ∩ B ⇒ x ∈ A and x ∉ B ⇒ x ∈ (A – B) 3. x ∈ [(A ∩ B) ∪ (A – B)] ⇒ (x ∈ A and x ∉ B) or (x ∈ A and x ∈ B′) ⇒ x ∈ A and x ∈ B and x ∈ B′ ⇒ x ∈ A and x ∈ B ∩ B′ ⇒ x ∈ A and x ∈ ϕ ⇒ x ∈ A ∪ ϕ ⇒ x ∈ A Hence (1) is incorrect. |
|