Prove the following

Question:

Let $X=\{n \in N: 1 \leq n \leq 50\}$. If

$A=\{n \in X: n$ is a multiple of 2$\}$ and

$\mathrm{B}=\{\mathrm{n} \in \mathrm{X}: \mathrm{n}$ is a multiple of 7$\}$, then the number of elements in the smallest subset of $\mathrm{X}$ containing both $A$ and $B$ is_________.

Solution:

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