## Formulas and Quick Tricks for Venn Diagram (Set Theory)

- Total = A + B + C – Both AB – Both BC – Both CA + None + ABC
- n (A ∪ B) = n (A) + n (B) – n (A ∩ B)

## Questions and Answers on Venn Diagram (Set Theory)

**Q.1:** Look at the Venn Diagram and answer the following questions:

A. People speaking English.

B. People speaking Hindi.

C. People speaking Punjabi.

D. People speaking all 3 languages.

E. People speaking only English.

F. People speaking only Hindi.

G. People speaking only Punjabi.

H. People speaking both English and Hindi.

I. People speaking both Hindi and Punjabi.

J. People speaking both Punjabi and English.

K. People speaking only English and Hindi.

L. People speaking only Hindi and Punjabi.

M. People speaking only Punjabi and English.

N. People speaking None of the languages.

O. People speaking both English and Hindi but not Punjabi.

P. People speaking both Hindi and Punjabi but not English.

Q. People speaking both Punjabi and English but not Hindi.

**Answer: **A. 28, B. 30, C. 35, D. 6, E. 10, F. 15, G. 18, H. 11, I. 10, J. 13, K. 5, L. 4, M. 7, N. 10, O. 5, P. 4, Q. 7

**Explanation: **Watch the Venn Diagram (Set Theory) Video for full explanation
__Venn Diagram (Set Theory) – Basic Concepts, Formulas, Math Tricks, Quantitative Aptitude Questions and Solutions__

**Q.2:** A survey from 200 students were asked, about the languages they speak. 100 students speak English, 130 speak Hindi and 80 speak Punjabi. 50 students speak English and Hindi, 50 speak Hindi and Punjabi, 30 speak Punjabi and English. 10 people speak all the three languages.

A. Students speaking English.

B. Students speaking Hindi.

C. Students speaking Punjabi.

D. Students speaking None of the languages.

**Answer: **A. 20, B. 40, C. 10, D. 20

**Explanation: **Watch the Venn Diagram (Set Theory) Video for full explanation
**Q.3:** In a class of 80 students, 25 like Physics, 35 like Math's and 10 like both. How many like either of them and how many like neither of them?

**Answer: **A. 20, B. 40, C. 10, D. 20

**Explanation: **Watch the Venn Diagram (Set Theory) Video for full explanation
**Q.4:** In a group of 150 people, people whose identity proof was verified, some had Driver’s License and some had Pan cards and some both. 80 people had Driver’s License and 50 had both. How many had Pan cards only?

**Answer: **A. 20, B. 40, C. 10, D. 20

**Explanation: **Watch the Venn Diagram (Set Theory) Video for full explanation