MAT - VENN DIAGRAMS - MCQs -1

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Interactive MCQ Worksheet • Clear, distinct and labelled diagrams

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Instructions: Select one answer for each question. Click Submit to check the worksheet. Correct questions turn green; incorrect or unanswered questions turn red. Use each question's Answer and View Explanation buttons to study the solution.

Question 1 – Sun, Star and Moon

1. Which Venn diagram best represents the relationship among Sun, Star and Moon?

(A) Diagram A (B) Diagram B (C) Diagram C (D) Diagram D

Correct Answer: (C)

Explanation: The Sun is a star, so the set Sun is contained within the set Stars. The Moon is neither the Sun nor a star, so it is represented by a separate circle. Thus Sun ⊂ Stars, with Moon separate.

Question 2 – Farmers, Educated People and Village People

2. In the diagram, triangle = farmers, circle = educated people and rectangle = people living in villages. Which number represents farmers who are educated and live in villages?

The common region of all three shapes contains 7.

(A) 10 (B) 4 (C) 9 (D) 7

Correct Answer: (D) 7

Explanation: We need people who are farmers AND educated AND living in villages. Therefore we look only at the region common to the triangle, circle and rectangle. That common region contains 7.

Question 3 – Birds, Crow and Cats

3. Which Venn diagram best represents the relationship among Birds, Crow and Cats?

(A) Diagram A (B) Diagram B (C) Diagram C (D) Diagram D

Correct Answer: (B)

Explanation: A crow is a type of bird, so Crow ⊂ Birds. Cats are not birds, so Cats must be a separate set. Therefore diagram B is correct.

Question 4 – Singers who are males but not doctors

4. How many singers are there who are males but not doctors?

(A) 14(B) 5(C) 11(D) 10

Correct Answer: (D) 10

Explanation: “Males but not doctors” means the region inside the Male circle and Singer triangle, but outside the Doctors rectangle. That region contains 10.

Question 5 – Doctors, singers and males

5. How many doctors are also singers and males?

(A) 5(B) 10(C) 11(D) 14

Correct Answer: (C) 11

Explanation: We need the people who belong to Doctors ∩ Singers ∩ Males. This is the region common to all three shapes. Its number is 11.

Question 6 – Males neither doctors nor singers

6. How many males are there who are neither doctors nor singers?

(A) 25(B) 60(C) 55(D) 90

Correct Answer: (A) 25

Explanation: “Neither doctors nor singers” means we take the part of the Male circle only, excluding both the rectangle and triangle. That region contains 25.

Question 7 – Males who are doctors but not singers

7. How many males are there who are doctors but not singers?

(A) 14(B) 11(C) 10(D) 5

Correct Answer: (D) 5

Explanation: We need the region inside the Male circle and Doctors rectangle, but outside the Singer triangle. The number there is 5.

Question 8 – Letters in exactly one figure

8. Which group of letters is present in exactly one of the geometric figures?

Exactly-one regions: B (circle only), F (rectangle only), H (triangle only).

(A) D, B, F(B) D, B, A(C) B, F, H(D) E, G, A

Correct Answer: (C) B, F, H

Explanation: A letter is “exactly one” when it lies inside only one geometric figure. B is in the circle only, F is in the rectangle only, and H is in the triangle only. Hence B, F, H.

Question 9 – Mathematics only

9. Triangle = Physics, Rectangle = Chemistry, Circle = Mathematics. How many students passed in Mathematics only?

(A) 3(B) 5(C) 4(D) 11

Correct Answer: (B) 5

Explanation: “Mathematics only” means the part inside the Mathematics circle but outside both Physics and Chemistry. The number in that region is 5.

Question 10 – Fathers, Grandfathers and Males

10. Which Venn diagram best represents the relationship among Fathers, Grandfathers and Males?

(A) Diagram A(B) Diagram B(C) Diagram C(D) Diagram D

Correct Answer: (A)

Explanation: Every grandfather is a father, and every father is a male. Therefore Grandfathers ⊂ Fathers ⊂ Males. Three nested circles represent this relationship.

Question 11 – Males, Maths Teachers and Sports Coaches

11. Triangle = Males, Square = Maths Teachers, Circle = Sports Coaches. Which letter represents males who are Maths teachers but not sports coaches?

(A) E(B) F(C) D(D) B

Correct Answer: (A) E

Explanation: We need a region inside the triangle (Male) and square (Maths Teacher), but outside the circle (Sports Coach). That region is labelled E.

Question 12 – Fractions, Rational Numbers and Whole Numbers

12. Which Venn diagram best represents the school-level relationship among Fractions, Rational Numbers and Whole Numbers?

(A) Diagram A(B) Diagram B(C) Diagram C(D) Diagram D

Correct Answer: (B)

Explanation: The textbook treats Rational Numbers as the larger set and represents Fractions and Whole Numbers as separate groups within it. Therefore, among the given options, diagram (B) is the intended answer. This follows the conventional school-level reasoning classification used in the supplied question.

NMMS Class 8 • Logical Venn Diagrams • Practice Worksheet