Question

A) There are 100 students who play at least one of volleyball, soccer and hockey, of these 50 play au three games, 84 play soccer, 73 play volleyball 62 play both soccer and hockey, 58 play volley ball and hockey and 62 play volleyball and soccer.

i) how many play volleyball only?
ii) how many play hockey only?​

Answer 1

i) 3

ii) 5

Explanation:

Let H be the set of students who play Hokey

V be the set of students who play Volleyball

S be the set of students who play Soccer

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card(volleyball only) = card(V) - [card(V∩H∩S) + card(V∩H only) + card(V∩S only)]

= 73 - [50 + (58-50) + (62-50)]

= 73 - [50 + 8 + 12]

= 73 - 70

= 3

………………………………………………

Card(Hokey only) = 100 - [3 + 8 + 50 + 10 + 12 + 12]

= 100 - 95

= 5

…………………

Note :

A Venn diagram might be helpful in such case.