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Question

If $A comma B$ and $C$ are three non-empty sets such that $A$ and $B$ are disjoint and the number of elements contained in $A$ is equal to those contained in the set of elements common to the sets $A$ and $C comma$ then $n left parenthesis A union B union C right parenthesis$ is necessarily equal to

(a) $n (B \cup C)$
$n (A \cup C)$
Both ((a) and ((b)
None of these

The correct answer is: (a) $n left parenthesis B union C right parenthesis$

We have,
$A intersection B equals ϕ blank a n d blank A subset of C$
$rightwards double arrow A intersection B equals ϕ blank a n d blank A union C equals C$
$therefore n open parentheses A union B union C close parentheses equals n open parentheses A union C union B close parentheses equals n open parentheses C union B close parentheses equals n left parenthesis B union C right parenthesis$

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