13.5 Exercises

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 $\{3,6,9\}$

4. Write a verbal description of the set $\{a,i,e,0,u\}$

5. Is $\{1,3,5\}$ a subset of the set of odd integers?

6. Is $\{A,B,C\}$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.

$$A=\{1,2,3,4,5\}B=\{1,3,5\}C=\{4,6\}U=\{\text{ numbers from }0\text{ to }10\}$$

7. $3\in B$

8. $5\in C$

9. $B\subset A$

10. $C\subset A$

11. $C\subset B$

12. $C\subset U$

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

13. $A\cup B$

14. $A\cup C$

15. $A\cap C$

16. $B\cap C$

17. $A^c$

18. $B^c$

Let $$D=\{b,a,c,k\},E=\{t,a,s,k\},F=\{b,a,t,h\}$$. Using these sets, find the following:

19. $D^c\cap E$

20. $F^c\cap D$

21. $(D\cap E)\cup F$

22. $D\cap (E\cup P)$

23. $(F\cap E{)}^c\cap D$

24. $(D\cup E{)}^c\cap F$

Create a Venn diagram to illustrate each of the following:

25. $(F\cap E)\cup D$

26. $(D\cup E{)}^c\cap F$

27. $(F^c\cap E^{\prime })\cap D$

28. $(D\cup E)\cup F$

Write an expression for the shaded region.

29.

30.

31.

32.

Let $$A=\{1,2,3,4,5\}B=\{1,3,5\}C=\{4,6\}$$. Find the cardinality of the given set.

33. $n(A)$

34. $n(B)$

35. $n(A\cup C)$

36. $n(A\cap C)$

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

37. $n(A\cap C)$

38. $n(B\cup C)$

39. $n(A\cap B\cap C^2)$

40. $n(A\cap B^c\cap C)$

41. If $$n(G)=20,n(H)=30,n(G\cap H)=5,$$ find $n(G\cup H)$

42. If $$n(G)=5,n(H)=8,n(G\cap H)=4,$$ find $n(G\cup H)$

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.

$$\begin{array}{cc}\text{52 only use Netflix}\hfill & \text{62 only use Redbox}\hfill \\ \text{24 only use a video store}\hfill & \text{16 use only a video store and Redbox}\hfill \\ \text{48 use only Netflix and Redbox}\hfill & \text{30 use only a video store and Netflix}\hfill \\ \text{10 use all three}\hfill & \text{25 use none of these}\hfill \end{array}$$

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?

$$\begin{array}{cc}\text{5 only said color}\hfill & \text{8 only said size}\hfill \\ \text{16 only said brand}\hfill & \text{20 said only color and size}\hfill \\ \text{42 said only color and brand}\hfill & \text{53 said only size and brand}\hfill \\ \text{102 said all three}\hfill & \text{20 said none of these}\hfill \end{array}$$

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.

$$\begin{array}{cc}\text{18 had seen The Matrix (M)}\hfill & \text{24 had seen Star Wars (SW)}\hfill \\ \text{20 had seen Lord of the Rings (LotR)}\hfill & \text{10 had seen M and SW}\hfill \\ \text{14 had seen LotR and SW }\hfill & \text{12 had seen M and LotR}\hfill \end{array}$$

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.

$$\begin{array}{cc}\text{30\% use the bus}\hfill & \text{20\% ride a bicycle}\hfill \\ \text{25\% walk}\hfill & \text{5\% use the bus and ride a bicycle}\hfill \\ \text{10\% ride a bicycle and walk}\hfill & \text{12\% use the bus and walk}\hfill \end{array}$$

Adapted from Math in Society by David Lippman, hosted on LibreTexts (math.libretexts.org) and licensed under CC BY-SA 3.0. Changes were made. License: CC-BY-SA-3.0.