First slide

Operations on Sets

Question

A college awarded 38 medals in football, 15 in basket ball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports, how many received medals in exactly two of the three sprots is

Moderate

A

9
B

18
C

27
D

3

Solution

Let F, B, C denote the set of men who received medals in football, basketball and cricket respectively.
$n (F \cap B) + n (B \cap C) + n (C \cap F) = 18$
$\Rightarrow a + d + b + d + c + d = 18$
$(∵ d = n (F \cap B \cap C) = 3)$
$a + b + c = 9$

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