Answer to Question #278788 in Discrete Mathematics for Freedi

Question

In a school, 100 students have access to three software packages A, B and C.

28 did not use any software

8 used only packages A

26 used only packages B

7 used only packages C

10 used all three packages

13 used both A and B

If twice as many students used package B as package A, Using Venn Diagram:

1. Calculate the no. of students using packages A & C only but not B.

2. Calculate the no. of students using packages C & B only but not A.

Answer 1

Let

$$N(A)=8+3+10+x$$

$$N(B)=26+3+10+y$$

$$N(C)=7+x+10+y$$

Then

$$N(A\cup B\cup C)=8+7+26+3+x+y+10$$

$$=100-28$$

$$x+y=18$$

If twice as many students used package B as package A

$$26+3+10+y=2(8+3+10+x)$$

$$y=2x+3$$

Then

$$x+2x+3=18$$

$$x=5$$

$$y=13$$

1.

$$N((A\cap C)-B)=x=5$$

2.

$$N((C\cap B)-A)=y=13$$