Relations and Functions

Question

In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

Solution

Set A = set of people who play cricket
Set B = set of people who play tennis
$space space space space space space space space space space space space space space rightwards double arrow space space space space straight n left parenthesis straight A union straight B right parenthesis space equals space 65$ ....(i)

n(A) = 40 ....(ii)
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Using, $space space space space space space space space space space space space space space space straight n left parenthesis straight A union straight B right parenthesis space equals space straight n left parenthesis straight A right parenthesis space plus straight n left parenthesis straight B right parenthesis minus straight n left parenthesis straight A intersection straight B right parenthesis comma space we space get$
65 = 40 + n(B) -10
$rightwards double arrow$ n(B) = 65 - 40 + 10 = 35
Hence, (a) Number of people who play tennis = n(B) = 35
Number of people who play tennis only = n(B-A)
$space space space space space space space space space space space space space space space space space space space space space space space equals space straight n left parenthesis straight B right parenthesis space minus straight n left parenthesis straight A intersection straight B right parenthesis space equals space 35 minus 10 equals 25$

Numbers	Closed under
	Addition	Subtraction	Multiplication	Division
Rational numbers	Yes	Yes		No
Integers		Yes		No
Whole numbers	...		Yes
Natural numbers		No

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