Answer to Question #203077 in Discrete Mathematics for Arafeen

Question

There are 70 women in class. Each play at least one game of the following games; volleyball, basketball, table tennis.

20 play volleyball only,10 play basketball only and 6 play table tennis.

4 play all the games and an equal number play 2 games only.

A) Illustration these informations on a Vern diagram.

i) Find the number of women who play volleyball.

Answer 1

Let

$$N(V\cap B\cap T')=N(V\cap T\cap B')=N(T\cap B\cap V')=x$$

Given

$$V(V\cup B\cup T)=70$$

$$V(V\cap B\cap T)=4$$

$$N(V\cap B'\cap T')=20$$

$$N(B\cap V'\cap T')=10$$

$$N(T\cap V'\cap B')=6$$

Then

$$20+10+6+4+3x=70$$

$$x=10$$

$$N(V)=10+4+10+10=34$$

34 women play volleyball.