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Question

$A$ and $B$ are any two non-empty sets and $A$ is proper subset of $B.$ If $n open parentheses A close parentheses equals 5 comma$ then find the minimum possible value of $n left parenthesis A increment B right parenthesis$

Is 1
Is 5
Cannot be determined
None of these

The correct answer is: Is 1

It is given that $A$ is a proper subset of $B$
$therefore A minus B equals ϕ rightwards double arrow n left parenthesis A minus B right parenthesis equals 0$
We have, $n open parentheses A close parentheses equals 5.$ So, minimum number of elements in $B$ is 6
Hence, the minimum possible value of $n left parenthesis A blank capital delta blank B right parenthesis$ is $n open parentheses B close parentheses minus n open parentheses A close parentheses equals 6 minus 5 equals 1$

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