Question

In a class of 50 students, 22 like History, 25 like Geography and 10 like both subjects. Draw
a Venn diagram and find the number of students who
(1) do not like History (ii) do not like Geography
(lit) like neither History nor Geography​

Answer 1

Therefore,

a) 28

b) 25

c) 3

Answer 2

(1) 28 students do not like history.

(2) 25 students do not like geography.

(3) 13 students neither like History nor Geography.

Step-by-step explanation:

Given:

1. Total number of students in class = 50 = a + b + c + d
2. The number of students that like History = 22 = a + b
3. The number of students that like Geography = 25 = b + c
4. The number of students that like both = 10 = b ( Hence a = 22 - 10 = 12)

(1) Now, finding the number of students who do not like history =  c + d

Subtracting equation 2 from 1, we get, c + d = 50 -22 = 28

Thus, 28 students do not like history.

(2) Now, finding the number of students who do not like Geography =  a + d

Subtracting equation 3 from 1, we get, a + d = 50 - 25 = 25

Thus, 25 students do not like geography.

(3) Now, finding the number of students who neither like History nor Geography =  d

From solution (2) above, a + d = 25 and from equation (4), a = 12.

So, d = 25 - 12 = 13

Thus, 13 students neither like History nor Geography.