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If $A=\{a, b, c\}, B=\{b, c, d\}$ and $C=\{a, d, c\}$ then $(A-B) \times(B \cap C)$ is equal to
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The correct answer is:
$\{(a, c),(a, d)\}$
Given, $A=\{a, b c\}, B=\{b, c, d\}$ and $C=\{a, d, c\}$
Now, $A-B=\{a, b, c\}-\{b, c, d\}=\{a\}$
and $B \cap C=\{b, c, d\} \cap\{a, d, c\}=\{c, d\}$
$\therefore(A-B) \times(B \cap C)=\{a\} \times\{c, d\}=\{(a, c),(a, d)\}$
Now, $A-B=\{a, b, c\}-\{b, c, d\}=\{a\}$
and $B \cap C=\{b, c, d\} \cap\{a, d, c\}=\{c, d\}$
$\therefore(A-B) \times(B \cap C)=\{a\} \times\{c, d\}=\{(a, c),(a, d)\}$
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