JEE Mains · Maths · STD 11 - 1. set theory
Let \(\mathrm{X}=\{\mathrm{n} \in \mathrm{N}: 1 \leq \mathrm{n} \leq 50\} .\) If \(A=\{n \in X: n \text { is a multiple of } 2\}\) and \(\mathrm{B}=\{\mathrm{n} \in \mathrm{X}: \mathrm{n} \text { is a multiple of } 7\},\) then the number of elements in the smallest subset of \(X\) containing both \(\mathrm{A}\) and \(\mathrm{B}\) is
- A \(29\)
- B \(26\)
- C \(31\)
- D \(34\)
Answer & Solution
Correct Answer
(A) \(29\)
Step-by-step Solution
Detailed explanation
\(\mathrm{n}(\mathrm{A})=25\) \(\mathrm{n}(\mathrm{B})=7\) \(\mathrm{n}(\mathrm{A} \cap \mathrm{B})=3\) \(n(A \cup B)=25+7-3=29\)
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