KCET · Maths · Sets and Relations
\(A\) 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
- 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
Answer & Solution
Correct Answer
(B) Statement (1) is false, statement (II) is true
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & |A|=3 \\ & |B|=6 \\ & |A \cup B|=|A|+|B|-|A \cap B| \\ & \min |A \cup B|=|A|+|B|-\max |A \cap B| \\ & =3+6-3=6 \\ & |A \cap B|=|A|+|B|-|A \cup B| \\ & \max |A \cap B|=|A|+|B|-\min |A \cup B| \\ & =3+6-6=3\end{aligned}\)
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