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Question

Given $n open parentheses U close parentheses equals 20 comma blank n open parentheses A close parentheses equals 12 comma blank n open parentheses B close parentheses equals 9 comma n open parentheses A intersection B close parentheses equals 4$ , where $U$ is the universal set, $A$ and $B$ are subsets of $U$ , then $n left square bracket open parentheses A union B close parentheses to the power of c end exponent right square bracket$ equals to

10
9
11
3

The correct answer is: 3

$n open parentheses A union B close parentheses equals n open parentheses A close parentheses plus n open parentheses B close parentheses minus n left parenthesis A intersection$
$equals 12 plus 9 minus 4 equals 17$
Hence, $n open square brackets left parenthesis A U B close parentheses to the power of c end exponent right square bracket equals n open parentheses U close parentheses minus n left parenthesis A union B right parenthesis$
$equals 20 minus 17 equals 3$

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