TIFR CSE 2010 | Part A | Question: 15

Question

Let $A, B$ be sets. Let $\bar{A}$ denote the compliment of set $A$ (with respect to some fixed universe), and $( A - B)$ denote the set of elements in $A$ which are not in $B$. Set $(A - (A - B))$ is equal to:

• A. $B$
• B. $A\cap \bar{B}$
• C. $A - B$
• D. $A\cap B$
• E. $\bar{B}$

Comments

@Arjun sir on the GO PDF, option B looks like option D. Can you fix this for future copies ? See the screenshot

Answer 1

$(A - (A - B)) = A ∩ (A ∩ B')'  $  Since $A-B=A∩B'$

                  $=$ $A ∩ (A' U B) $     Since $(A∩B)'$ = $A'UB'  $

                  $=$ $A ∩ B$ Option $D$

Answer 2

I hope this might be useful

Answer 3

(A - (A - B)) = A - (AB') = A(AB')'  = A(A'+B) = AB = A∩B

Option (D) A∩B , is the correct answer.