Analyzing Sets with Venn Diagrams

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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 19 | Questions: 20 | Updated: Jan 21, 2026
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Question 1 / 21
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1) In a Venn diagram, the universal set U is represented by a rectangle enclosing all circles.

Explanation

The rectangle is the sample space containing all outcomes.

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About This Quiz
Analyzing Sets With Venn Diagrams - Quiz

How do sets overlap, combine, or differ? In this quiz, you’ll visualize relationships between sets using Venn diagrams. Take this quiz to practice set theory with a visual edge.

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2) If two events are disjoint, then P(A ∪ B) = P(A)+P(B).

Explanation

For disjoint sets, A ∩ B = ∅, so formula simplifies.

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3) In a Venn diagram, the shaded region outside set A represents:

Explanation

The complement A′ = elements not in A.

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4) Which region is shaded in A ∪ B but not A ∩ B?

Explanation

This is the symmetric difference.

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5) If A′ ∩ B is shaded, this means:

Explanation

A′ ∩ B = elements in B but not in A.

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6) In a survey of 100 people, 60 like tea, 50 like coffee, and 20 like both. How many like neither?

Explanation

Tea ∪ Coffee=60+50−20=90. Neither=100−90=10.

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7) For any set A, A ∪ A′ = U.

Explanation

A and its complement cover the universal set.

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8) In a Venn diagram, the overlapping region of two circles A and B represents:

Explanation

The shaded overlap is the intersection, i.e., elements in both sets.

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9) The union A ∪ B is represented by:

Explanation

Union means all elements in A, B, or both.

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10) If n(A)=10, n(B)=15, n(A ∩ B)=5, then n(A ∪ B)=?

Explanation

n(A ∪ B) = n(A)+n(B)−n(A ∩ B) = 10+15−5=20.

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11) If P(A)=0.4, P(B)=0.5, P(A ∩ B)=0.2, then P(A ∪ B)=?

Explanation

Apply formula: 0.4+0.5−0.2=0.7.

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12) In a class of 40 students, 20 study math, 18 study physics, and 10 study both. How many study math or physics?

Explanation

n(A ∪ B)=20+18−10=28.

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13) If P(A)=0.3, P(B)=0.4, and A and B are disjoint, then P(A ∪ B)=?

Explanation

No overlap → 0.3+0.4=0.7.

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14) If n(U)=50, n(A)=30, then n(A′)=?

Explanation

A′ = U−A = 50−30=20.

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15) If P(A)=0.4, P(B)=0.3, P(A ∩ B)=0.1, then P(A ∪ B)=?

Explanation

P(A ∪ B)=0.4+0.3−0.1=0.6.

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16) In a group of 200 students, 120 take biology, 80 take chemistry, and 50 take both. How many take biology or chemistry?

Explanation

n(A ∪ B)=120+80−50=150.

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17) The addition rule P(A∪B)=P(A)+P(B)−P(A∩B)P(A ∪ B)=P(A)+P(B)−P(A ∩ B)P(A∪B)=P(A)+P(B)−P(A∩B) corrects for:

Explanation

Without subtracting, the intersection would be counted twice.

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18) In a Venn diagram with three circles A, B, and C, the very center overlap represents:

Explanation

The triple overlap is the intersection of all three sets.

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19) P(A ∪ B) ≤ P(A) + P(B).

Explanation

The intersection is subtracted, so union ≤ sum.

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20) If A and B are mutually exclusive, then:

Explanation

Disjoint sets → no overlap, addition rule simplifies.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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In a Venn diagram, the universal set U is represented by a rectangle...
If two events are disjoint, then P(A ∪ B) = P(A)+P(B).
In a Venn diagram, the shaded region outside set A represents:
Which region is shaded in A ∪ B but not A ∩ B?
If A′ ∩ B is shaded, this means:
In a survey of 100 people, 60 like tea, 50 like coffee, and 20 like...
For any set A, A ∪ A′ = U.
In a Venn diagram, the overlapping region of two circles A and B...
The union A ∪ B is represented by:
If n(A)=10, n(B)=15, n(A ∩ B)=5, then n(A ∪ B)=?
If P(A)=0.4, P(B)=0.5, P(A ∩ B)=0.2, then P(A ∪ B)=?
In a class of 40 students, 20 study math, 18 study physics, and 10...
If P(A)=0.3, P(B)=0.4, and A and B are disjoint, then P(A ∪ B)=?
If n(U)=50, n(A)=30, then n(A′)=?
If P(A)=0.4, P(B)=0.3, P(A ∩ B)=0.1, then P(A ∪ B)=?
In a group of 200 students, 120 take biology, 80 take chemistry, and...
The addition rule P(A∪B)=P(A)+P(B)−P(A∩B)P(A ∪...
In a Venn diagram with three circles A, B, and C, the very center...
P(A ∪ B) ≤ P(A) + P(B).
If A and B are mutually exclusive, then:
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