Q61 / 180 · COMEDK 2016 · Mathematics

If $A=\{a, b, c\}, B=\{b, c, d\}$ and $C=\{a, d, c\}$, then $(A-B) \times(B \cap C)=$

  • A
    $\{(a, c),(a, d),(b, d)\}$
  • B
    $\{(c, a),(d, a)\}$
  • C
    $\{(a, b),(c, d)\}$
  • Correct answer
    D
    $\{(a, c),(a, d)\}$

Solution

Given that, $A=\{a, b, c\}, B=\{b, c, d\}$ and $c=\{a, d, c\}$ Now, $\boldsymbol{A}-B=\{a, b, c\}-\{b, c, d\}=\{a\}$ and $B \cap C=\{b, c, d\} \cap\{a, d, c\}=\{c, d\}$ $(A-B) \times(B \cap C)=\{a\} \times\{c, d\}=\{(a, c),(a, d)\}$

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

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