Q62 / 180 · KCET 2025 · Mathematics

$A$ and $B$ are two sets having 3 and 6 elements respectively. Consider the following statements. Statement (I): Minimum number of elements in AUB is 3 Statement (II): Maximum number of elements in AB is 3 Which of the following is correct?

  • A
    Statement (I) is true, statement (II) is false
  • Correct answer
    B
    Statement (1) is false, statement (II) is true
  • C
    Both statements (1) and (II) are true
  • D
    Both statements (I) and (II) are false

Solution

$\begin{aligned} & |A|=3 \\ & |B|=6 \\ & |A \cup B|=|A|+|B|-|A \cap B| \\ & \min |A \cup B|=|A|+|B|-\max |A \cap B| \\ & =3+6-3=6 \\ & |A \cap B|=|A|+|B|-|A \cup B| \\ & \max |A \cap B|=|A|+|B|-\min |A \cup B| \\ & =3+6-6=3\end{aligned}$

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

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