Q. In a class of 60 students, 23 play Hockey 15 Play Basket-ball and 20 play cricket. 7 play Hockey and Basket-ball, 5 play cricket and Basket-ball, 4 play Hockey and Cricket and 15 students do not play any of these games. Then
Sets
Solution:
a + e + f + g = 23
b + d + f + g = 15
c + d + e + g = 20
f + g = 7; d + g = 5
e + g = 4
a + b + c + d + e + f + g = 60 - 15 = 45
By substitutions,
a + e = 16, b + d = 8, b + f = 10, c + e = 15, c + d = 16
Also, b + c + d = 22
a + c + e = 30, a + b + f = 25
From these, we get
b = 6, a = 15, c = 14 e = 1, d = 2, f = 4 and g = 3
Clearly(a) is not correct
for (b) a + f = 19 $\Rightarrow $ (b)is incorrect
for (c) e = 1 $\Rightarrow $ (c) is correct
