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1.Set Theory
medium
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
$34$
(JEE MAIN-2020)
Solution
$\mathrm{n}(\mathrm{A})=25$
$\mathrm{n}(\mathrm{B})=7$
$\mathrm{n}(\mathrm{A} \cap \mathrm{B})=3$
$n(A \cup B)=25+7-3=29$
Standard 11
Mathematics
