Q41 / 125 · BITSAT 2014 · Mathematics

The set $(A \backslash B) \cup(B \backslash A)$ is equal to]

  • A
    $[A \backslash(A \cap B)] \cap[B \backslash(A \cap B)]$
  • Correct answer
    B
    $(A \cup B) \backslash(A \cap B)$
  • C
    $A \backslash(A \cap B)$
  • D
    $\overrightarrow{A \cap B} \backslash A \cup B$

Solution

Given set can be written as $(A-B) \cup(B-A)=(A \cup B)-(A \cap B)$ (By definition of symmetric difference) Hence, $(\mathrm{A} \backslash \mathrm{B}) \cup(\mathrm{B} \backslash \mathrm{A})=(\mathrm{A} \cup \mathrm{B}) \backslash(\mathrm{A} \cap \mathrm{B})$

Hence, the correct answer is option: 'B'.

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