In a class there are 27 students. Out of these 14 study Psychology and 19 study Geography. There are 11 students who study both Psychology and Geography.

(1) How many students study Psychology but not Geography ?

1. 3
2. 4
3. 5
4. 6

(2) How many students study Geography but not Psychology ?

1. 7
2. 8
3. 9
4. 11

(3) How many students study neither Psychology nor Geography ?

1. 8
2. 7
3. 6
4. 5

(4) What is the difference between the number of students who study Psychology only and those who study Geography only ?

1. 4
2. 5
3. 6
4. 7

Given:

Total students: n(U) = 27

Students studying Psychology: n(P) = 14

Students studying Geography: n(G) = 19

Students studying both: n(P ∩ G) = 11

(1) This represents the number of students who study Psychology only.

We use the formula:

n(P - G) = n(P) - n(P ∩ G)

Substituting the values in above, we get:

n(P - G) = 14 - 11

n(P - G) = 3

Number of students who study Psychology but not Geography = 3.

Hence, option 1 is the correct option.

(2) This represents the number of students who study Geography only.

We use the formula:

n(G - P) = n(G) - n(P ∩ G)

Substituting the values in above, we get:

n(G - P) = 19 - 11

n(G - P) = 8

Number of students who study Geography but not Psychology = 8.

Hence, option 2 is the correct option.

(3) First, find the total students who study at least one subject (n(P ∪ G)):

n(P ∪ G) = n(P) + n(G) - n(P ∩ G)

Substituting the values in above, we get:

n(P ∪ G) = 14 + 19 - 11

n(P ∪ G) = 33 - 11

n(P ∪ G) = 22

So, 22 students study either of two subjects.

To find students who study neither Psychology nor Geography, we use formula:

Students who study neither Psychology nor Geography = Total students - Students who study either of two subjects

Students who study neither Psychology nor Geography = 27 - 22

Students who study neither Psychology nor Geography = 5

Hence, option 4 is the correct option.

(4) Difference between the number of students who study Psychology only and those who study Geography only = ?

Number of students who study Psychology only = 3.

Number of students who study Geography only = 8.

Difference = 8 - 3 = 5

Difference between the number of students who study Psychology only and those who study Geography only = 5.

Hence, option 2 is the correct option.