Q16 / 50 · Manipal (MET) 2022 · Mathematics

If $A=\{1,2\}, \quad B=\{1,2,3,4\}, \quad C=\{5,6\} \quad$ and $D=\{5,6,7,8\}$, then state which of the following is true?

  • Correct answer
    A
    $(A \times C) \subset(B \times D)$
  • B
    $A \times B \subset C \times D$
  • C
    $(A \times B) \subset(A \times D)$
  • D
    $A \times C \subset B \times D$

Solution

Here, $\begin{aligned} A \times C= & \{1,2\} \times\{5,6\} \\ = & \{(1,5),(1,6),(2,5),(2,6)\} \\ \text { and } B \times D= & \{1,2,3,4\} \times\{5,6,7,8\} \\ = & \{(1,5),(1,6),(1,7),(1,8),(2,5),(2,6), \\ & (2,7),(2,8),(3,5),(3,6),(3,7),(3,8), \\ & (4,5),(4,6),(4,7),(4,8)\} \\ \therefore \quad(A \times C) \subset & (B \times D) \end{aligned}$

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

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