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If $A=\{2,3\}, B=\{4,5\}, C=\{5,6\}$, then what is the number of elements of $A \times(B \cap C)$ ?
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The correct answer is:
2
Given $\mathrm{A}=\{2,3\}, \mathrm{B}=\{4,5\}, \mathrm{C}=\{5,6\}$
: $B \cap C=\{5\}$
$\Rightarrow \quad A \times(B \cap C)=\{2,3\} \times\{5\}=\{(2,5),(3,5)\}$
Hence, required number of elements in $A \times(B \cap C)=2$
: $B \cap C=\{5\}$
$\Rightarrow \quad A \times(B \cap C)=\{2,3\} \times\{5\}=\{(2,5),(3,5)\}$
Hence, required number of elements in $A \times(B \cap C)=2$
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