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WBJEE · Maths · Sets and Relations

For any two sets \(\mathrm{A}\) and \(\mathrm{B}, \mathrm{A}-(\mathrm{A}-\mathrm{B})\) equals

  1. A \(\mathrm{B}\)
  2. B \(\mathrm{A}-\mathrm{B}\)
  3. C \(\mathrm{A} \cap \mathrm{B}\)
  4. D \(\mathrm{A}^{\mathrm{C}} \cap \mathrm{B}^{\mathrm{C}}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\mathrm{A} \cap \mathrm{B}\)

Step-by-step Solution

Detailed explanation

Hints: \(A-(A-B)=A-\left(A \cap B^c\right)=A \cap\left(A \cap B^c\right)^c=A \cap\left(A^c \cup B\right)=\left(A \cap A^c\right) \cup(A \cap B)=A \cap B\)