1.2.0: Exercises

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Jan 2, 2025
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- 1.2: Subsets
- 1.3: Understanding Venn Diagrams

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For the following exercises, list all the proper subsets of each set.

1. {chocolate, vanilla, strawberry}
2. {true, false }

3. {mother, father, daughter, son }

$\{7\}$

For the following exercises, determine the relationship between the two sets and write the relationship symbolically.

$D=\{0,1,2, \ldots, 9\}, A=\{0,2,4,6,8\}, B=\{1,3,5,7,9\}, C=\{8,6,4,2,0\}, Z=\{0\}$ , and $\emptyset$

5. $D$ and $A$

6. $B$ and $D$

7. $C$ and $D$

8. $Z$ and $C$

9. $Z$ and $\emptyset$

10. $A$ and $B$

11. $A$ and $C$

12. $\emptyset$ and $D$

13. $B$ and $C$

14. $A$ and $Z$

For the following exercises, calculate the total number of subsets of each set.

15. {Adele, Beyonce, Cher, Madonna, Shakira }

16. { Art, Paul }

17. {Peter, Paul, Mary}

18. $\emptyset$

19. $\{3\}$

20. $\{l, o, v, e\}$

21. $\}$

22. \{football, baseball, basketball, soccer, hockey, tennis, golf\}

23. Set $A$ , if $n(A)=12$ .

24. Set $B$ , if $n(B)=9$ .

For the following exercises, use the set of letters in the word largest as the set,

$U = \left\{ \text{l, a, r, g, e, s, t} \right\}$ .

25. Find a subset of $U$ that is equivalent, but not equal, to the set: $\{l, \mathrm{a}, \mathrm{s}, \mathrm{t}\}$ .

26. Find a subset of $U$ that is equal to the set: $\{l, \mathrm{a}, \mathrm{s}, \mathrm{t}\}$ .

27. Find a subset of $U$ that is equal to the set: $\{\mathrm{a}, \mathrm{r}, \mathrm{t}\}$ .

28. Find a subset of $U$ that is equivalent, but not equal, to the set $\{\mathrm{a}, \mathrm{r}, \mathrm{t}, \mathrm{s}\}$ .

29. Find a subset of $U$ that is equivalent, but not equal, to the set: $\{\mathrm{r}, \mathrm{a}, \mathrm{t}, \mathrm{e}, \mathrm{s}\}$ .

30. Find a subset of $U$ that is equal to the set: $\{\mathrm{r}, \mathrm{a}, \mathrm{t}, \mathrm{e}, \mathrm{s}\}$ .

31. Find two three-character subsets of set $U$ that are equivalent, but not equal, to each other.

32. Find two three-character subsets of set $U$ that are equal to each other.

33. Find two five-character subsets of set $U$ that are equal to each other.

34. Find two five-character subsets of set $U$ that are equivalent, but not equal, to each other.

Find two equal subsets of /**/U/**/ with a cardinality of 4.

35. Find two equivalent subset of

$U$ with a cardinality of 7 .

36. Find two equal subsets of

$U$ with a cardinality of 4 .

37. Find a subset of

$U$ that is equivalent, but not equal to,

$\{0,3,6,9, \ldots\}$ .

38. Find a subset of

$U$ that is equivalent, but not equal to,

$\{-1,-4,-9,-16,-25, \ldots\}$ .

39. True or False. The set of natural numbers,

$\mathbb{N}=\{1,2,3, \ldots\}$ , is equivalent to set

$U$ .

40. True or False. Set

$U$ is an equivalent subset of the set of rational numbers,

$\mathbb{Q}=\left\{\left.\frac{p}{q} \right\rvert\, p\right.$ and

$q$ are integers and

$\left.q \neq 0.\right\}$ .

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