For any two sets A and B, A−(A−B) equals: - Vidyadip

MCQ

For any two sets $A$ and $\ce{B, A−(A−B)}$ equals:

A
$B$
B
$A − B$
✓
$A ∩ B$
D
$A^C ∩ B^C$

✓

Answer

Correct option: C.

$A ∩ B$

Now, $\ce{A − (A − B) = A − (A ∩ B^C)}$
$= \ce{A ∩ (A ∩ B^C)^C}$
$= \ce{A ∩(A^C∪ B)}$
$= \ce{(A ∩ A^C) ∪ (A ∩ B)}$
$= \ce{A ∩ B}$

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