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SETS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSETS1 Mark
MCQ
For any two sets $A$ and $B, A−(A−B)$ equals:
  • A
    $B$
  • B
    $A − B$
  • ✓
    $A ∩ B$
  • D
    $A^C ∩ B^C$
✓

Answer

Correct option: C.
$A ∩ B$
  1. $A ∩ B$
Solution:
$\text { Now, } A-(A-B)=A-\left(A \cap B^C\right)$
$ =A \cap\left(A \cap B^C\right)^C$
$ =A \cap\left(A^C \cup B\right)$
$ =\left(A \cap A^C\right) \cup(A \cap B)$
$ =A \cap B$

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