Question

A, B and C are three restaurants in Taman Damai. A group of residents in Taman Damai were asked to name the restaurants they like.

The Venn diagram shows part of the results of the survey.

Given:
A = {residents who like restaurant A}
B = {residents who like restaurant B}
C = {residents who like restaurant C}
It is given that 20 residents like restaurant A
or B, 22 residents like restaurant B or C and
7 residents do not like restaurant A or C.
Calculate the number of residents who
(a) like restaurant C only.
(b) like restaurant A but do not like restaurant B.
(c) do not like restaurant A or B.

Please help me to solve this question and explain it to me.Thanks.(｡･ω･｡)
Silly answer will be report. ​

Answer 1

(a) 5

(b) 10

(c) 10

Explanation:

There are 20 people who like A or B. There are 4+6=10 people who like B, so there are 10 people who like A but not B (the region of the Venn diagram that is outside B and inside A). This answers part b.

Since there are 3 people who like A only, there are 10−3=7 people who like A and C but not B (the intersection of A and C that is outside B).

Next, there are 22 people who like B or C. There are 4+6=10 people who like B, and 7 people who like A and C but not B. Therefore, there are 22−10−7=5 people who like C only. This answers part a.

Finally, there are 7 people who don't like A or C (the region of the diagram that is outside of the circles but inside the rectangle). And as previously found, there are 5 people who like C only. So the number of people who don't like A or B (but may or may not like C) is 7+5=12.