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Mathematics LibreTexts

7.5: Exercises

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1. List out the elements of the set “The letters of the word Mississipi”

2. List out the elements of the set “Months of the year”

3. Write a verbal description of the set

4. Write a verbal description of the set

5. Is a subset of the set of odd integers?

6. Is a subset of the set of letters of the alphabet?

For problems 7-12, consider the sets below, and indicate if each statement is true or false.

7.

8.

9.

10.

11.

12.

Using the sets from above, and treating as the Universal set, find each of the following:

13.

14.

15.

16.

17.

18.

Let . Using these sets, find the following:

19.

20.

21.

22.

23.

24.

Create a Venn diagram to illustrate each of the following:

25.

26.

27.

28.

Write an expression for the shaded region.

29.

A Venn diagram with 3 circles overlapping, labeled A, B, and C. The region where B overlaps either or both of the other sets is highlighted.

30.

A Venn diagram with 3 circles overlapping, labeled A, B, and C. The region in B alone is highlighted, where it isn't overlapping either other set.

31.

A Venn diagram with 3 circles overlapping, labeled A, B, and C. The highlighted region includes all of C, combined with the portion of A that doesn't overlap B.

32.

A Venn diagram with 3 circles overlapping, labeled A, B, and C. The highlighted region includes the part of A that doesn't overlap with C, combined with the part of B that doesn't overlap C, combined with the overlap of all three circles.

Let . Find the cardinality of the given set.

33.

34.

35.

36.

The Venn diagram here shows the cardinality of each set. Use this in 37-40 to find the cardinality of given set.

A Venn diagram of three overlapping circles labeled A, B, and C.  The part only in A is 7. The overlap of A and B only is 3. The part in B only is 5.  The overlap of A and C only is 4. The overlap of all three is 1. The overlap of B and C only is 2. The part in C only is 8. The part outside all three is 6.

37.

38.

39.

40.

41. If find

42. If find

43. A survey was given asking whether they watch movies at home from Netflix, Redbox, or a video store. Use the results to determine how many people use Redbox.

44. A survey asked buyers whether color, size, or brand influenced their choice of cell phone. The results are below. How many people were influenced by brand?

45. Use the given information to complete a Venn diagram, then determine: a) how many students have seen exactly one of these movies, and b) how many had seen only Star Wars.

46. A survey asked people what alternative transportation modes they use. Using the data to complete a Venn diagram, then determine: a) what percent of people only ride the bus, and b) how many people don’t use any alternate transportation.


This page titled 7.5: Exercises is shared under a CC BY-SA license and was authored, remixed, and/or curated by David Lippman (The OpenTextBookStore) .

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