Venn Diagrams Quiz � Apply the Addition Rule & Interpret Set Relationships (HSS.CP.B.7)

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

Only A

Only B

A′

Elements in A or B but not both

This is the symmetric difference.

Explanation

This is the symmetric difference.

2) For any set A, A ∪ A′ = U.

True

False

A and its complement cover the universal set.

Explanation

A and its complement cover the universal set.

3) The union A ∪ B is represented by:

Only the overlap

Only A

A and B together including overlap

Only B

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

Explanation

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

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

A ∪ B

A ∩ B

A′

B′

The complement A′ = elements not in A.

Explanation

The complement A′ = elements not in A.

5) In a Venn diagram, the universal set U is represented by a rectangle enclosing all circles.

True

False

The rectangle is the sample space containing all outcomes.

Explanation

The rectangle is the sample space containing all outcomes.

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

True

False

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

Explanation

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

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

0.7

0.1

0.12

0.5

No overlap → 0.3+0.4=0.7.

Explanation

No overlap → 0.3+0.4=0.7.

8) If A′ ∩ B is shaded, this means:

In A only

In B only but not A

In both A and B

Outside A and B

A′ ∩ B = elements in B but not in A.

Explanation

A′ ∩ B = elements in B but not in A.

9) If n(U)=50, n(A)=30, then n(A′)=?

30

20

50

15

A′ = U−A = 50−30=20.

Explanation

A′ = U−A = 50−30=20.

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

10

20

30

40

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

Explanation

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

11) 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:

Double-counting the union

Double-counting the intersection

Adding complements

Subtracting universal set

Without subtracting, the intersection would be counted twice.

Explanation

Without subtracting, the intersection would be counted twice.

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

20

25

30

15

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

Explanation

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

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

28

38

30

40

n(A ∪ B)=20+18−10=28.

Explanation

n(A ∪ B)=20+18−10=28.

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

0.6

0.7

0.5

0.8

P(A ∪ B)=0.4+0.3−0.1=0.6.

Explanation

P(A ∪ B)=0.4+0.3−0.1=0.6.

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

150

200

250

100

n(A ∪ B)=120+80−50=150.

Explanation

n(A ∪ B)=120+80−50=150.

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

0.7

0.9

1.1

0.6

Apply formula: 0.4+0.5−0.2=0.7.

Explanation

Apply formula: 0.4+0.5−0.2=0.7.

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

A ∪ B

A ∩ B

A′

Universal set

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

Explanation

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

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

A ∪ B ∪ C

A ∩ B

A ∩ B ∩ C

A′ ∩ B′ ∩ C′

The triple overlap is the intersection of all three sets.

Explanation

The triple overlap is the intersection of all three sets.

19) P(A ∪ B) ≤ P(A) + P(B).

True

False

The intersection is subtracted, so union ≤ sum.

Explanation

The intersection is subtracted, so union ≤ sum.

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

P(A ∩ B)=0

P(A ∪ B)=P(A)+P(B)

Both a and b

Neither

Disjoint sets → no overlap, addition rule simplifies.

Explanation

Disjoint sets → no overlap, addition rule simplifies.

Analyzing Sets with Venn Diagrams

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

2)

What first name or nickname would you like us to use?

2) For any set A, A ∪ A′ = U.

3) The union A ∪ B is represented by:

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

5) In a Venn diagram, the universal set U is represented by a rectangle enclosing all circles.

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

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

8) If A′ ∩ B is shaded, this means:

9) If n(U)=50, n(A)=30, then n(A′)=?

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

11) 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:

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

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

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

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

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

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

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

19) P(A ∪ B) ≤ P(A) + P(B).

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