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Question

Let $U$ be the universal set for sets $A$ and $B$ such that $n open parentheses A close parentheses equals 200 comma n open parentheses B close parentheses equals 300$ and $n open parentheses A intersection B close parentheses equals 100.$ Then, $n left parenthesis A ´ intersection B ´ right parenthesis$ is equal to 300, provided that $n left parenthesis blank U right parenthesis$ is equal to

600
700
800
900

The correct answer is: 700

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

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parallel

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Statement 2:91 is composite number

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Statement 2:91 is composite number

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Statement 1:The numbers $square root of 2 comma blank square root of 3 comma blank square root of 5$ cannot be the terms of a single A.P. with non-zero common difference
Statement 2:If $p comma blank q comma blank r left parenthesis p not equal to q right parenthesis$ are terms (not necessarily consecutive) of an A.P., then there exists a rational number $k$ such that $left parenthesis r minus q right parenthesis divided by left parenthesis q minus p right parenthesis equals k$

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