1.3.1: Exercises

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

3. {mother, father, daughter, son }

4. \(\{7\}\)

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.

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 \(\left.q \neq 0.\right\}\).