WBJEE · Maths · Sets and Relations
For any two sets \(\mathrm{A}\) and \(\mathrm{B}, \mathrm{A}-(\mathrm{A}-\mathrm{B})\) equals
- A \(\mathrm{B}\)
- B \(\mathrm{A}-\mathrm{B}\)
- C \(\mathrm{A} \cap \mathrm{B}\)
- D \(\mathrm{A}^{\mathrm{C}} \cap \mathrm{B}^{\mathrm{C}}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{A} \cap \mathrm{B}\)
Step-by-step Solution
Detailed explanation
Hints: \(A-(A-B)=A-\left(A \cap B^c\right)=A \cap\left(A \cap B^c\right)^c=A \cap\left(A^c \cup B\right)=\left(A \cap A^c\right) \cup(A \cap B)=A \cap B\)
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