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Maths-

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Easy

Question

In a class of 35 students, 17 have taken Mathematics, 10 have taken Mathematics but not Economics. If each student has taken either Mathematics or Economics or both, then the number of students who have taken Economics but not Mathematics is

(a) 7
25
18
32

The correct answer is: 18

Let $M$ and $E$ denote the sets of students who have taken Mathematics and Economics respectively. Then, we have
$n open parentheses M union E close parentheses equals 35 comma n open parentheses M close parentheses equals 17 blank a n d blank n open parentheses M intersection E to the power of ´ end exponent close parentheses equals 10$
Now,
$n open parentheses M intersection E to the power of ´ end exponent close parentheses equals n open parentheses M close parentheses minus n left parenthesis M intersection E right parenthesis$
$rightwards double arrow 10 equals 17 minus n open parentheses M intersection E close parentheses rightwards double arrow n open parentheses M intersection E close parentheses equals 7$
Now,
$n open parentheses M union E close parentheses equals n open parentheses M close parentheses plus n open parentheses E close parentheses minus n left parenthesis M intersection E right parenthesis$
$rightwards double arrow 35 equals 17 plus n open parentheses E close parentheses minus 7 rightwards double arrow n open parentheses E close parentheses equals 25$
$therefore n open parentheses E intersection M to the power of ´ end exponent close parentheses equals n open parentheses E close parentheses minus n open parentheses E intersection M close parentheses equals 25 minus 7 equals 18$

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