100+ Venn Diagram MCQs for Competitive Exams
Practice these Venn Diagram questions for Railway, SSC, Banking, Police, Defence and other competitive examinations. The set covers union, intersection, complements, subsets, two-set and three-set problems, and exam-style numerical questions.
1. In a Venn diagram, the universal set is generally represented by which shape?
The rectangle encloses all elements under consideration and represents the universal set.
2. The symbol ∪ represents which set operation?
Union contains every element belonging to either set or to both sets.
3. The symbol ∩ represents which set operation?
Intersection contains only the elements common to the given sets.
4. If A and B have no common element, then A and B are called:
Disjoint sets have no common elements; therefore, their intersection is empty.
5. Which region represents elements belonging to A but not to B?
A−B contains elements that are in A and excluded from B.
6. If A is completely inside B in a Venn diagram, which relation is shown?
A circle inside B indicates that every element of A also belongs to B.
7. The common region of three sets A, B and C is represented by:
The triple intersection contains elements common to all three sets.
8. Which part shows elements belonging to neither A nor B?
Elements outside both circles but inside the universal-set rectangle belong to neither set.
9. If A={1,2,3} and B={3,4,5}, then A∩B is:
Only 3 is common to both sets, so the intersection is {3}.
10. If A={1,2,3} and B={3,4,5}, then A∪B contains how many elements?
The union is {1,2,3,4,5}, which has five distinct elements.
11. In a survey, 40 candidates know subject A, 25 know subject B and 10 know both. How many know at least one subject?
Using n(A∪B)=n(A)+n(B)−n(A∩B), the answer is 40+25−10=55.
12. If 40 candidates know subject A and 10 know both A and B, how many know A only?
A-only candidates = total in A − candidates in both = 40−10=30.
13. If 25 candidates know subject B and 10 know both A and B, how many know B only?
B-only candidates = total in B − candidates in both = 25−10=15.
14. In a survey, 60 candidates know subject A, 35 know subject B and 15 know both. How many know at least one subject?
Using n(A∪B)=n(A)+n(B)−n(A∩B), the answer is 60+35−15=80.
15. If 60 candidates know subject A and 15 know both A and B, how many know A only?
A-only candidates = total in A − candidates in both = 60−15=45.
16. If 35 candidates know subject B and 15 know both A and B, how many know B only?
B-only candidates = total in B − candidates in both = 35−15=20.
17. In a survey, 75 candidates know subject A, 45 know subject B and 20 know both. How many know at least one subject?
Using n(A∪B)=n(A)+n(B)−n(A∩B), the answer is 75+45−20=100.
18. If 75 candidates know subject A and 20 know both A and B, how many know A only?
A-only candidates = total in A − candidates in both = 75−20=55.
19. If 45 candidates know subject B and 20 know both A and B, how many know B only?
B-only candidates = total in B − candidates in both = 45−20=25.
20. In a survey, 80 candidates know subject A, 50 know subject B and 30 know both. How many know at least one subject?
Using n(A∪B)=n(A)+n(B)−n(A∩B), the answer is 80+50−30=100.
21. If 80 candidates know subject A and 30 know both A and B, how many know A only?
A-only candidates = total in A − candidates in both = 80−30=50.
22. If 50 candidates know subject B and 30 know both A and B, how many know B only?
B-only candidates = total in B − candidates in both = 50−30=20.
23. In a survey, 90 candidates know subject A, 55 know subject B and 25 know both. How many know at least one subject?
Using n(A∪B)=n(A)+n(B)−n(A∩B), the answer is 90+55−25=120.
24. If 90 candidates know subject A and 25 know both A and B, how many know A only?
A-only candidates = total in A − candidates in both = 90−25=65.
25. If 55 candidates know subject B and 25 know both A and B, how many know B only?
B-only candidates = total in B − candidates in both = 55−25=30.
26. In a survey, 100 candidates know subject A, 65 know subject B and 30 know both. How many know at least one subject?
Using n(A∪B)=n(A)+n(B)−n(A∩B), the answer is 100+65−30=135.
27. If 100 candidates know subject A and 30 know both A and B, how many know A only?
A-only candidates = total in A − candidates in both = 100−30=70.
28. If 65 candidates know subject B and 30 know both A and B, how many know B only?
B-only candidates = total in B − candidates in both = 65−30=35.
29. In a survey, 50 candidates know subject A, 32 know subject B and 12 know both. How many know at least one subject?
Using n(A∪B)=n(A)+n(B)−n(A∩B), the answer is 50+32−12=70.
30. If 50 candidates know subject A and 12 know both A and B, how many know A only?
A-only candidates = total in A − candidates in both = 50−12=38.
31. If 32 candidates know subject B and 12 know both A and B, how many know B only?
B-only candidates = total in B − candidates in both = 32−12=20.
32. In a survey, 70 candidates know subject A, 40 know subject B and 18 know both. How many know at least one subject?
Using n(A∪B)=n(A)+n(B)−n(A∩B), the answer is 70+40−18=92.
33. If 70 candidates know subject A and 18 know both A and B, how many know A only?
A-only candidates = total in A − candidates in both = 70−18=52.
34. If 40 candidates know subject B and 18 know both A and B, how many know B only?
B-only candidates = total in B − candidates in both = 40−18=22.
35. In a survey, 48 candidates know subject A, 28 know subject B and 9 know both. How many know at least one subject?
Using n(A∪B)=n(A)+n(B)−n(A∩B), the answer is 48+28−9=67.
36. If 48 candidates know subject A and 9 know both A and B, how many know A only?
A-only candidates = total in A − candidates in both = 48−9=39.
37. If 28 candidates know subject B and 9 know both A and B, how many know B only?
B-only candidates = total in B − candidates in both = 28−9=19.
38. In a survey, 120 candidates know subject A, 75 know subject B and 25 know both. How many know at least one subject?
Using n(A∪B)=n(A)+n(B)−n(A∩B), the answer is 120+75−25=170.
39. If 120 candidates know subject A and 25 know both A and B, how many know A only?
A-only candidates = total in A − candidates in both = 120−25=95.
40. If 75 candidates know subject B and 25 know both A and B, how many know B only?
B-only candidates = total in B − candidates in both = 75−25=50.
41. In a survey, 65 candidates know subject A, 42 know subject B and 17 know both. How many know at least one subject?
Using n(A∪B)=n(A)+n(B)−n(A∩B), the answer is 65+42−17=90.
42. If 65 candidates know subject A and 17 know both A and B, how many know A only?
A-only candidates = total in A − candidates in both = 65−17=48.
43. If 42 candidates know subject B and 17 know both A and B, how many know B only?
B-only candidates = total in B − candidates in both = 42−17=25.
44. In a survey, 85 candidates know subject A, 50 know subject B and 20 know both. How many know at least one subject?
Using n(A∪B)=n(A)+n(B)−n(A∩B), the answer is 85+50−20=115.
45. If 85 candidates know subject A and 20 know both A and B, how many know A only?
A-only candidates = total in A − candidates in both = 85−20=65.
46. If 50 candidates know subject B and 20 know both A and B, how many know B only?
B-only candidates = total in B − candidates in both = 50−20=30.
47. In a survey, 55 candidates know subject A, 30 know subject B and 8 know both. How many know at least one subject?
Using n(A∪B)=n(A)+n(B)−n(A∩B), the answer is 55+30−8=77.
48. If 55 candidates know subject A and 8 know both A and B, how many know A only?
A-only candidates = total in A − candidates in both = 55−8=47.
49. If 30 candidates know subject B and 8 know both A and B, how many know B only?
B-only candidates = total in B − candidates in both = 30−8=22.
50. In a survey, 95 candidates know subject A, 60 know subject B and 35 know both. How many know at least one subject?
Using n(A∪B)=n(A)+n(B)−n(A∩B), the answer is 95+60−35=120.
51. If 95 candidates know subject A and 35 know both A and B, how many know A only?
A-only candidates = total in A − candidates in both = 95−35=60.
52. If 60 candidates know subject B and 35 know both A and B, how many know B only?
B-only candidates = total in B − candidates in both = 60−35=25.
53. In a survey, 110 candidates know subject A, 70 know subject B and 28 know both. How many know at least one subject?
Using n(A∪B)=n(A)+n(B)−n(A∩B), the answer is 110+70−28=152.
54. If 110 candidates know subject A and 28 know both A and B, how many know A only?
A-only candidates = total in A − candidates in both = 110−28=82.
55. If 70 candidates know subject B and 28 know both A and B, how many know B only?
B-only candidates = total in B − candidates in both = 70−28=42.
56. Out of 100 candidates, 60 chose A, 50 chose B and 30 chose both. How many chose neither?
First find the union: 60+50−30=80. Therefore, neither = 100−80=20.
57. Out of 100 candidates, 60 chose A, 50 chose B and 30 chose both. How many chose exactly one?
Exactly one = A-only + B-only = (60−30)+(50−30)=50.
58. Out of 80 candidates, 45 chose A, 35 chose B and 15 chose both. How many chose neither?
First find the union: 45+35−15=65. Therefore, neither = 80−65=15.
59. Out of 80 candidates, 45 chose A, 35 chose B and 15 chose both. How many chose exactly one?
Exactly one = A-only + B-only = (45−15)+(35−15)=50.
60. Out of 70 candidates, 42 chose A, 28 chose B and 12 chose both. How many chose neither?
First find the union: 42+28−12=58. Therefore, neither = 70−58=12.
61. Out of 70 candidates, 42 chose A, 28 chose B and 12 chose both. How many chose exactly one?
Exactly one = A-only + B-only = (42−12)+(28−12)=46.
62. Out of 60 candidates, 38 chose A, 25 chose B and 10 chose both. How many chose neither?
First find the union: 38+25−10=53. Therefore, neither = 60−53=7.
63. Out of 60 candidates, 38 chose A, 25 chose B and 10 chose both. How many chose exactly one?
Exactly one = A-only + B-only = (38−10)+(25−10)=43.
64. Out of 150 candidates, 90 chose A, 75 chose B and 40 chose both. How many chose neither?
First find the union: 90+75−40=125. Therefore, neither = 150−125=25.
65. Out of 150 candidates, 90 chose A, 75 chose B and 40 chose both. How many chose exactly one?
Exactly one = A-only + B-only = (90−40)+(75−40)=85.
66. Out of 200 candidates, 120 chose A, 95 chose B and 55 chose both. How many chose neither?
First find the union: 120+95−55=160. Therefore, neither = 200−160=40.
67. Out of 200 candidates, 120 chose A, 95 chose B and 55 chose both. How many chose exactly one?
Exactly one = A-only + B-only = (120−55)+(95−55)=105.
68. Out of 90 candidates, 55 chose A, 40 chose B and 20 chose both. How many chose neither?
First find the union: 55+40−20=75. Therefore, neither = 90−75=15.
69. Out of 90 candidates, 55 chose A, 40 chose B and 20 chose both. How many chose exactly one?
Exactly one = A-only + B-only = (55−20)+(40−20)=55.
70. Out of 75 candidates, 48 chose A, 32 chose B and 16 chose both. How many chose neither?
First find the union: 48+32−16=64. Therefore, neither = 75−64=11.
71. Out of 75 candidates, 48 chose A, 32 chose B and 16 chose both. How many chose exactly one?
Exactly one = A-only + B-only = (48−16)+(32−16)=48.
72. If n(A∪B)=70, n(A)=45 and n(B)=40, find n(A∩B).
From n(A∪B)=n(A)+n(B)−n(A∩B), intersection = 45+40−70=15.
73. If n(A∪B)=80, n(A)=50 and n(B)=55, find n(A∩B).
From n(A∪B)=n(A)+n(B)−n(A∩B), intersection = 50+55−80=25.
74. If n(A∪B)=100, n(A)=65 and n(B)=60, find n(A∩B).
From n(A∪B)=n(A)+n(B)−n(A∩B), intersection = 65+60−100=25.
75. If n(A∪B)=55, n(A)=35 and n(B)=30, find n(A∩B).
From n(A∪B)=n(A)+n(B)−n(A∩B), intersection = 35+30−55=10.
76. If n(A∪B)=120, n(A)=75 and n(B)=70, find n(A∩B).
From n(A∪B)=n(A)+n(B)−n(A∩B), intersection = 75+70−120=25.
77. If n(A∪B)=90, n(A)=48 and n(B)=57, find n(A∩B).
From n(A∪B)=n(A)+n(B)−n(A∩B), intersection = 48+57−90=15.
78. If n(A∪B)=150, n(A)=95 and n(B)=80, find n(A∩B).
From n(A∪B)=n(A)+n(B)−n(A∩B), intersection = 95+80−150=25.
79. If n(A∪B)=60, n(A)=38 and n(B)=35, find n(A∩B).
From n(A∪B)=n(A)+n(B)−n(A∩B), intersection = 38+35−60=13.
80. A-only=18, B-only=12, and A∩B=7. If the universal set has 50 elements, how many are in neither set?
The union has 18+12+7=37 elements. Hence neither = 50−37=13.
81. A-only=18, B-only=12, and A∩B=7. Find n(A).
Set A consists of its exclusive region and the overlap: 18+7=25.
82. A-only=18, B-only=12, and A∩B=7. Find n(B).
Set B consists of its exclusive region and the overlap: 12+7=19.
83. A-only=25, B-only=15, and A∩B=10. If the universal set has 70 elements, how many are in neither set?
The union has 25+15+10=50 elements. Hence neither = 70−50=20.
84. A-only=25, B-only=15, and A∩B=10. Find n(A).
Set A consists of its exclusive region and the overlap: 25+10=35.
85. A-only=25, B-only=15, and A∩B=10. Find n(B).
Set B consists of its exclusive region and the overlap: 15+10=25.
86. A-only=14, B-only=9, and A∩B=6. If the universal set has 40 elements, how many are in neither set?
The union has 14+9+6=29 elements. Hence neither = 40−29=11.
87. A-only=14, B-only=9, and A∩B=6. Find n(A).
Set A consists of its exclusive region and the overlap: 14+6=20.
88. A-only=14, B-only=9, and A∩B=6. Find n(B).
Set B consists of its exclusive region and the overlap: 9+6=15.
89. A-only=30, B-only=20, and A∩B=8. If the universal set has 75 elements, how many are in neither set?
The union has 30+20+8=58 elements. Hence neither = 75−58=17.
90. A-only=30, B-only=20, and A∩B=8. Find n(A).
Set A consists of its exclusive region and the overlap: 30+8=38.
91. A-only=30, B-only=20, and A∩B=8. Find n(B).
Set B consists of its exclusive region and the overlap: 20+8=28.
92. A-only=22, B-only=17, and A∩B=5. If the universal set has 60 elements, how many are in neither set?
The union has 22+17+5=44 elements. Hence neither = 60−44=16.
93. A-only=22, B-only=17, and A∩B=5. Find n(A).
Set A consists of its exclusive region and the overlap: 22+5=27.
94. A-only=22, B-only=17, and A∩B=5. Find n(B).
Set B consists of its exclusive region and the overlap: 17+5=22.
95. A-only=16, B-only=13, and A∩B=4. If the universal set has 45 elements, how many are in neither set?
The union has 16+13+4=33 elements. Hence neither = 45−33=12.
96. A-only=16, B-only=13, and A∩B=4. Find n(A).
Set A consists of its exclusive region and the overlap: 16+4=20.
97. A-only=16, B-only=13, and A∩B=4. Find n(B).
Set B consists of its exclusive region and the overlap: 13+4=17.
98. A-only=28, B-only=19, and A∩B=9. If the universal set has 80 elements, how many are in neither set?
The union has 28+19+9=56 elements. Hence neither = 80−56=24.
99. A-only=28, B-only=19, and A∩B=9. Find n(A).
Set A consists of its exclusive region and the overlap: 28+9=37.
100. A-only=28, B-only=19, and A∩B=9. Find n(B).
Set B consists of its exclusive region and the overlap: 19+9=28.
To solve Venn Diagram questions quickly, identify the common region first, subtract overlaps carefully, and use the union formula for two sets or the inclusion–exclusion formula for three sets. Regular practice improves both speed and accuracy in competitive examinations.
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