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

1) 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.

2) 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.

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) 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.

6) 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.

7) 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.

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 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.

10) 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.

11) 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.

12) 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.

13) 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.

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) P(A ∪ B) ≤ P(A) + P(B).

True

False

The intersection is subtracted, so union ≤ sum.

Explanation

The intersection is subtracted, so union ≤ sum.

19) 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.

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) For any set A, A ∪ A′ = U.

2)

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

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

3) The union A ∪ B is represented by:

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

5) 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:

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

7) If n(U)=50, n(A)=30, then n(A′)=?

8) If A′ ∩ B is shaded, this means:

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

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

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

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

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

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) P(A ∪ B) ≤ P(A) + P(B).

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

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