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BITSAT 2023Paper 1
Exam
BITSAT
Year
2023
Paper
Paper 1
Subject
Mathematics
Chapter
Sets and Relations

BITSAT 2023 · Paper 1 · Mathematics · Sets and Relations

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

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

Options

  1. A3≤n(A∪B)≤63 \leq \mathrm{n}(\mathrm{A} \cup \mathrm{B}) \leq 6
  2. B3≤n(A∪B)≤93 \leq \mathrm{n}(\mathrm{A} \cup \mathrm{B}) \leq 9
  3. C6≤n(A∪B)≤96 \leq \mathrm{n}(\mathrm{A} \cup \mathrm{B}) \leq 9
  4. D0≤n(A∪B)≤90 \leq n(A \cup B) \leq 9

Correct answer

C. 6≤n(A∪B)≤96 \leq \mathrm{n}(\mathrm{A} \cup \mathrm{B}) \leq 9

Step-by-step solution

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