Q221 / 270 · NDA 2010 (Phase 2) · Mathematics

If $A=\{2,3\}, B=\{4,5\}, C=\{5,6\}$, then what is the number of elements in $A \times(B \cap C)$

  • Correct answer
    A
    2
  • B
    4
  • C
    6
  • D
    8

Solution

$\begin{aligned} & A=\{2,3\}, B=\{4,5\}, C=\{5,6\} \\ & B \cap C=\{5\} \\ & A \times(B \cap C)=\{2,3\} \times\{5\} \\ & =\{(2,5)(3,5) \\ & \therefore n\{A \times(B \cap C)\}=2 .\end{aligned}$

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

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