Two-Set Unions, Intersections, and Probabilities Quiz

1) For sets A and B, if |A|=28, |B|=19, and |A∩B|=7, then |A∪B| is:

34

40

48

54

28 + 19 − 7 = 40.

Explanation

28 + 19 − 7 = 40.

2) If |A∪B|=50, |A|=35, and |B|=29, then |A∩B| equals:

14

15

9

6

35 + 29 − 50 = 14.

Explanation

35 + 29 − 50 = 14.

3) For any finite sets A and B, max(|A|,|B|) ≤ |A∪B| ≤ |A|+|B|.

True

False

Union is at least each set, at most their sum.

Explanation

Union is at least each set, at most their sum.

4) In a finite universe U, the number of elements in neither A nor B is:

|A∪B|

|U|-|A∪B|

|U|-|A∩B|

|Aᶜ∪Bᶜ|

'Neither' means outside the union.

Explanation

'Neither' means outside the union.

5) If P(A)=0.6, P(B)=0.5, and P(A∩B)=0.3, then P(A∪B) is:

0.6

0.8

0.9

1.1

0.6 + 0.5 − 0.3 = 0.8.

Explanation

0.6 + 0.5 − 0.3 = 0.8.

6) In a universe of 100 elements, |A|=70 and |B|=45. Minimum |A∩B|?

0

10

15

25

Minimum intersection = 70 + 45 − 100 = 15.

Explanation

Minimum intersection = 70 + 45 − 100 = 15.

7) Which statements are true for any finite sets A and B?

|A∩B| ≤ |A|

|A∪B| ≥ |B|

|A∪B| ≥ |A∩B|

|A∪B| = |A| + |B| always

All true except (d) when sets overlap.

Explanation

All true except (d) when sets overlap.

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8) In a school of 90 students, 52 Drama, 41 Music, 20 both. How many in at least one?

63

73

81

90

52 + 41 − 20 = 73.

Explanation

52 + 41 − 20 = 73.

9) Library: 200 readers; 120 English, 90 Spanish, 50 neither. Borrow both?

40

60

70

90

|E∪S|=150; intersection=120+90−150=60.

Explanation

|E∪S|=150; intersection=120+90−150=60.

10) |Aᶜ ∪ Bᶜ| = |U| − |A∩B|.

True

False

By De Morgan, Aᶜ ∪ Bᶜ = (A∩B)ᶜ.

Explanation

By De Morgan, Aᶜ ∪ Bᶜ = (A∩B)ᶜ.

11) Match expressions with meanings:

∣A∪B∣

∣A∩B∣

∣Aᶜ∩Bᶜ∣

Union=at least one; intersection=both; complements intersection=neither.

Explanation

Union=at least one; intersection=both; complements intersection=neither.

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12) Universe 60: |A|=40, |B|=35, |A∩B|=20. Neither?

0

5

15

20

|A∪B|=55; 60−55=5.

Explanation

|A∪B|=55; 60−55=5.

13) 40 people: 30 in A, 25 in B, 5 in both. Possible?

True

False

30+25−5 = 50 > 40 impossible.

Explanation

30+25−5 = 50 > 40 impossible.

14) Probability exactly one of A, B occurs:

P(A)+P(B)

P(A∪B)

P(A)+P(B)-2P(A∩B)

P(A∩B)

Subtract double intersection for symmetric difference.

Explanation

Subtract double intersection for symmetric difference.

15) Class of 80: 55 Algebra, 50 Calculus, 15 fail both. Passed both?

30

35

40

45

Union=65; intersection=55+50−65=40.

Explanation

Union=65; intersection=55+50−65=40.

Two-Set Unions, Intersections, and Probabilities Quiz

1) For sets A and B, if |A|=28, |B|=19, and |A∩B|=7, then |A∪B| is:

2)

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

2) If |A∪B|=50, |A|=35, and |B|=29, then |A∩B| equals:

3) For any finite sets A and B, max(|A|,|B|) ≤ |A∪B| ≤ |A|+|B|.

4) In a finite universe U, the number of elements in neither A nor B is:

5) If P(A)=0.6, P(B)=0.5, and P(A∩B)=0.3, then P(A∪B) is:

6) In a universe of 100 elements, |A|=70 and |B|=45. Minimum |A∩B|?

7) Which statements are true for any finite sets A and B?

8) In a school of 90 students, 52 Drama, 41 Music, 20 both. How many in at least one?

9) Library: 200 readers; 120 English, 90 Spanish, 50 neither. Borrow both?

10) |Aᶜ ∪ Bᶜ| = |U| − |A∩B|.

11) Match expressions with meanings:

12) Universe 60: |A|=40, |B|=35, |A∩B|=20. Neither?

13) 40 people: 30 in A, 25 in B, 5 in both. Possible?

14) Probability exactly one of A, B occurs:

15) Class of 80: 55 Algebra, 50 Calculus, 15 fail both. Passed both?