Inclusion–Exclusion with Two Sets Quiz

1) For two sets A and B, the inclusion–exclusion formula is:

|A∪B|=|A|+|B|

|A∪B|=|A|+|B|-|A∩B|

|A∪B|=|A|-|B|

|A∪B|=|A∩B|

Subtract |A∩B| to correct for double counting.

Explanation

Subtract |A∩B| to correct for double counting.

2) If |A|=18, |B|=12, and |A∩B|=5, then |A∪B| equals:

25

30

35

40

18 + 12 – 5 = 25.

Explanation

18 + 12 – 5 = 25.

3) If |A∪B|=40, |A|=25, and |B|=22, then |A∩B| equals:

7

5

3

9

25 + 22 – 40 = 7.

Explanation

25 + 22 – 40 = 7.

4) If A and B are disjoint, then |A∪B| = |A| + |B|.

True

False

Disjoint sets have |A∩B|=0.

Explanation

Disjoint sets have |A∩B|=0.

5) For any sets A and B, |A∩B| ≤ |A| and |A∩B| ≤ |B|.

True

False

The intersection cannot exceed either set.

Explanation

The intersection cannot exceed either set.

6) In a survey, 30 students like coffee, 20 like tea, and 10 like both. How many like coffee or tea (or both)?

40

50

60

30

30 + 20 − 10 = 40.

Explanation

30 + 20 − 10 = 40.

7) If |A|=15, |B|=15, and |A∪B|=20, then |A∩B| equals:

10

5

15

0

15 + 15 – 20 = 10.

Explanation

15 + 15 – 20 = 10.

8) Among the numbers 1 to 60, how many are divisible by 4 or 6?

15

20

25

30

15 + 10 − 5 = 20.

Explanation

15 + 10 − 5 = 20.

9) If |A∪B| = |A| + |B|, then A and B must be disjoint.

True

False

Equality means |A∩B| = 0.

Explanation

Equality means |A∩B| = 0.

10) Which expression counts the elements that are in exactly one of A or B?

|A∪B|

|A|+|B|-2|A∩B|

|A|-|B|

|A∩B|

Subtract intersection twice to exclude shared elements.

Explanation

Subtract intersection twice to exclude shared elements.

11) A universal set U has 50 elements. If |A| = 30 and |Aᶜ| = x, then x equals:

30

20

50

10

Complement size = 50 - 30 = 20.

Explanation

Complement size = 50 - 30 = 20.

12) For two sets A and B, |A ∪ Bᶜ| = |U| − |B∖A|.

True

False

A ∪ Bᶜ is complement of B∖A.

Explanation

A ∪ Bᶜ is complement of B∖A.

13) 100 people: 60 like apples, 50 like bananas. Minimum liking both?

10

20

30

50

Minimum overlap = 60 + 50 − 100 = 10.

Explanation

Minimum overlap = 60 + 50 − 100 = 10.

14) Same group: maximum liking both apples & bananas?

10

40

50

60

Max overlap is min(60, 50) = 50.

Explanation

Max overlap is min(60, 50) = 50.

15) If |A|=15, |B|=10, and |A∩B|=0, then |A∪B|=25.

True

False

Disjoint sets add directly.

Explanation

Disjoint sets add directly.

Inclusion–Exclusion with Two Sets Quiz

1) For two sets A and B, the inclusion–exclusion formula is:

2)

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

2) If |A|=18, |B|=12, and |A∩B|=5, then |A∪B| equals:

3) If |A∪B|=40, |A|=25, and |B|=22, then |A∩B| equals:

4) If A and B are disjoint, then |A∪B| = |A| + |B|.

5) For any sets A and B, |A∩B| ≤ |A| and |A∩B| ≤ |B|.

6) In a survey, 30 students like coffee, 20 like tea, and 10 like both. How many like coffee or tea (or both)?

7) If |A|=15, |B|=15, and |A∪B|=20, then |A∩B| equals:

8) Among the numbers 1 to 60, how many are divisible by 4 or 6?

9) If |A∪B| = |A| + |B|, then A and B must be disjoint.

10) Which expression counts the elements that are in exactly one of A or B?

11) A universal set U has 50 elements. If |A| = 30 and |Aᶜ| = x, then x equals:

12) For two sets A and B, |A ∪ Bᶜ| = |U| − |B∖A|.

13) 100 people: 60 like apples, 50 like bananas. Minimum liking both?

14) Same group: maximum liking both apples & bananas?

15) If |A|=15, |B|=10, and |A∩B|=0, then |A∪B|=25.