Question:
Let $X=\{n \in N: 1 \leq n \leq 50\} .$ if
$A=\{n \in X: n$ is $a$ multiple of 2$\}$ and
$B=\{n \in X: n$ is $a$ multiple of 7$\}$, then the number of
elements in the smallest subset of $X$ containing both $A$ and $B$ is________.
Solution:
From the given conditions,
$n(A)=25, n(B)=7$ and $n(A \cap B)=3$
$n(A \cup B)=n(A)+n(B)-n(A \cap B)$
$=25+7-3=29$
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