Section SV.1 – Solutions to the Practice Problems

1. {M, i, s, p}

2. {January, February, March, April, May, June, July, August, September, October, November, December}

3. The set of numbers 3, 6, and 9.

4. The set of letters a, e, i, o, u.

5. The set of all natural numbers that are multiples of 3.

6.

a. Equal (order doesn’t matter)
b. Equal (repeats don’t matter)
c. Equal (order and repeats don’t matter)
d. Not equal (not the same elements)

7.

a. Equal (order doesn’t matter)
b. Not equal (not the same elements)
c. Equal repeats don’t matter)
d. Equal (order and repeats don’t matter)

8.

a. Not a set (not well defined)
b. Set
c. Set
d. Not a set (not well defined)

9.

a. Not a set (not well defined)
b. Set
c. Not a set (not well defined)
d. Set

10.

a. Finite (it is a very large number)
b. Infinite
c. Finite (equal to the set {1 ,2 ,3, 4, 5, 6, 7, 8, 9})
d. Infinite (the set follows the pattern forever)

11.

a. Finite (it may be changing but it is not infinite)
b. Infinite
c. Infinite
d. Finite (equal to the set of letters in the alphabet)

12.

a. ⊈
b. ⊆
c. ⊆
d. ⊆
e. ⊈
f. ⊈

13.

a. ⊆
b. ⊆ and ⊂ (both)
c. ⊆ and ⊂ (both)
d. neither

14. Yes

15. Yes

16. No, the Moon is not a planet

17. Yes

18.

a. False, the empty set has no elements.
b. False, it would mean the set containing the empty set.
c. True, the empty set is a subset of every set.

19.

a. true
b. false
c. true
d. false
e. false
f. true
g. false

20.

a. false
b. false
c. true
d. true
e. false
f. true
g. false

21.

a. ⊂ and ⊆
b. ∈
c. ⊆ and ⊇
d. ⊃ and ⊇
e. ⊂ and ⊆

22.

a. ⊂ and ⊆
b. ⊂ and ⊆
c. ⊃ and ⊇
d. ⊆ and ⊇
e. ∈

23. B ⊂ A

24.

a. true
b. false, the set containing 7 is not an element of A.
c. true
d. true
e. false
f. true

25. {a, b, c, d}, {a, b, c}, {b, c, d}, {a, c, d}, {a, b, d}, {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}, {a}, {b}, {c}, {d}, { }

26. {Luke, Lea}, {Luke, Han}, {Lea, Han}, {Luke}, {Lea}, {Han}, { }

27. {Stuart, Kevin}, {Kevin, Bob}, {Stuart, Bob}, {Stuart}, {Kevin}, {Bob}, { }

28. number of subsets = 2⁴ = 16, number of proper subsets = 15

29. number of subsets = 2⁷ = 128, number of proper subsets = 127

30. 2⁶ = 64 possible ways

31. 2⁷ = 128 possible ways