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Maths-

General

Easy

Question

Let $n open parentheses U close parentheses equals 700 comma blank n open parentheses A close parentheses equals 200 comma blank n open parentheses B close parentheses equals 300$ and $n open parentheses A intersection B close parentheses equals 100.$ Then, $n open parentheses A to the power of c end exponent intersection B to the power of c end exponent close parentheses equals$

(a) 400
600
300
200

The correct answer is: 300

We have,
$n left parenthesis A to the power of c end exponent intersection B to the power of c end exponent right parenthesis$
$equals n open curly brackets open parentheses A union B close parentheses to the power of c end exponent close curly brackets$
$equals n open parentheses U close parentheses minus n left parenthesis A union B right parenthesis$
$equals n open parentheses U close parentheses minus open curly brackets n open parentheses A close parentheses plus n open parentheses B close parentheses minus n open parentheses A intersection B close parentheses close curly brackets$
$equals 700 minus open parentheses 200 plus 300 minus 100 close parentheses equals 300$

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