Section SV.2 – Practice Problems
1. Suppose the universal set is U = {1, 2, 3, … , 8, 9, 10}. If A = {5, 6, 8}, find A̅
2. Suppose the universal set is U = {red, orange, yellow, green, blue, purple}.
If A = {red, green, blue}, find A̅
3. Suppose the universal set U is all even numbers from 2 to 20.
If A = {4, 6, 10, 16, 18, 20}, find A̅
4. Let U = {1, 2, 3, … , 18, 19, 20} be the universal set. Consider the sets:
A = {2, 3, 5, 7, 10, 11, 12, 13, 14, 16, 17, 19} B = {5, 10, 13, 14, 16, 19, 20}
Find each of the following:
a. A ⋃ B
b. A ⋂ B
c. A̅ ⋂ B
5. Let U = {1, 2, 3, … , 18, 19, 20} be the universal set. Consider the sets:
A = {6, 11, 12, 14, 16, 17, 18} B = {1, 4, 5, 8, 11, 12, 15, 16}
Find each of the following:
a. A ⋃ B
b. A ⋂ B
c. A ⋂ B̅
6. Let U = {1, 2, 3, … , 18, 19, 20} be the universal set. Consider the sets:
A = {1, 2, 3, 4, 6, 8, 9, 11, 12, 14, 15, 18} B = {5, 9, 12, 14, 17, 19, 20}
Find each of the following:
a. A ⋃ B
b. A ⋂ B
c. A̅ ⋂ B
7. Let U = {1, 2, 3, … , 8, 9, 10} be the universal set. Consider the sets:
A = {3, 5, 8, 10} B = {1, 3, 4, 7, 8, 9, 10} C = {2, 5, 6}
Find each of the following:
a. A ⋃ C
b. B ⋂ C
c. A ⋂ B̅
d. [latex]\overline{(A~\cup~C)}[/latex]
e. [latex]\overline{(A~\cap~B)}~\cup~C[/latex]
f. [latex](A~\cap~B)~\cap~(B~\cup~\bar{C})[/latex]
8. Let A and B be two sets. (hint: you do not need to know what the elements of A and B are to do this problem).
Find each of the following:
a. A ⋃ ∅
b. B ⋂ ∅
9. Let D = {b, a, c, k}, E = {t, a, s, k}, F = {b, a, t, h}, and U = set of letters in the alphabet.
Using these sets, find the following:
a. D̅ ⋂ E
b. F̅ ⋂ D
c. (D ⋂ E ) ⋃ F
d. D ⋂ (E ⋃ F )
e. [latex]\overline{(F~\cap~E)}~\cap~D[/latex]
f. [latex]\overline{(D~\cup~E)}~\cap~F[/latex]
g. [latex]\overline{(D~\cap~F)}~\cap~(D~\cup~E)[/latex]
10. Let U = {Gru, Dave, Jerry, Mark, Phil, Kevin, Josh, Stuart, Carl}, A = {Gru, Stuart, Kevin}, B = {Gru, Dave, Jerry, Mark, Phil}, and C={Gru, Phil, Josh, Carl}. Using these sets, write a set operation expression for each of the answers below.
a. {Gru}
b. {Gru, Dave, Jerry, Mark, Phil, Kevin, Stuart}
c. {Dave, Jerry, Mark}
