Q34 / 100 · BITSAT 2023 (Memory Based Paper 1) · Mathematics

A set $A$ has 3 elements and another set B has 6 elements. Then

  • A
    $3 \leq \mathrm{n}(\mathrm{A} \cup \mathrm{B}) \leq 6$
  • B
    $3 \leq \mathrm{n}(\mathrm{A} \cup \mathrm{B}) \leq 9$
  • Correct answer
    C
    $6 \leq \mathrm{n}(\mathrm{A} \cup \mathrm{B}) \leq 9$
  • D
    $0 \leq n(A \cup B) \leq 9$

Solution

We have
$\min n(A \cup B)=\max \{n(A), n(B)\}=\max \{3,6\}=6$
$\operatorname{Max} n(A \cup B)=n(A)+n(B)=9$
$\therefore 6 \leq n(A \cup B) \leq 9$

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

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