Section 4.1 Sets
247
57. Consider the following subsets of the set of all students:
A = set of all computer science majors
B = set of all physics majors
C = set of all science majors
D = set of all female students
Using set operations, describe each of the following sets in terms of A, B, C, and D:
a. set of all students not majoring in science
b. set of all female physics majors
c. set of all students majoring in both computer science and physics
d. set of all male computer science majors
58. Consider the following subsets of the set of all students:
A = set of all computer science majors
B = set of all physics majors
C = set of all science majors
D = set of all female students
Using set operations, describe each of the following sets in terms of A, B, C, and D:
a. set of all male students who are not physics majors
b. set of all science majors who are not computer science majors
c. set of all students who are female or science majors
d. set of all students who are science majors but are neither computer science nor physics majors
59. Write the set expression for the desired results of the Web search query for sites pertaining to dogs that are
not retrievers (Exercise 31, Section 1.1). Assume that D = set of dog pages, R = set of retriever pages.
60. Write the set expression for the desired results of the Web search query for sites pertaining to oil paintings
by Van Gogh or Rembrandt but not Vermeer (Exercise 32, Section 1.1). Assume that O = set of oil painting pages, G = set of Van Gogh pages, R = set of Rembrandt pages, V = set of Vermeer pages.
61. Write the set expression for the desired results of the Web search query for sites pertaining to novels or
plays about AIDS (Exercise 33, Section 1.1). Assume that N = set of novel pages, P = set of play pages,
A = set of AIDS pages.
62. Write the set expression for the desired results of the Web search query for sites pertaining to coastal
wetlands in Louisiana but not in Alabama (Exercise 34, Section 1.1). Assume that C = set of coastal
wetlands pages, L = set of Louisiana pages, A = set of Alabama pages.
63. Which of the following statements are true for all sets A, B, and C?
a. A c A = A
d. (A′)′ = A
b. B d B = B
e. A − B = (B − A)′
c. (A d B)′ = A′ d B′
f. (A − B) d (B − A) = [
64. Which of the following statements are true for all sets A, B, and C?
a. If A d B = [, then A ( B.
d. [ d {[} = [
b. B × A = A × B
e. (A − B) c (B − C ) = A − C
c. [ × A = [
f. (A − C ) d (A − B) = A − (B c C )
247
57. Consider the following subsets of the set of all students:
A = set of all computer science majors
B = set of all physics majors
C = set of all science majors
D = set of all female students
Using set operations, describe each of the following sets in terms of A, B, C, and D:
a. set of all students not majoring in science
b. set of all female physics majors
c. set of all students majoring in both computer science and physics
d. set of all male computer science majors
58. Consider the following subsets of the set of all students:
A = set of all computer science majors
B = set of all physics majors
C = set of all science majors
D = set of all female students
Using set operations, describe each of the following sets in terms of A, B, C, and D:
a. set of all male students who are not physics majors
b. set of all science majors who are not computer science majors
c. set of all students who are female or science majors
d. set of all students who are science majors but are neither computer science nor physics majors
59. Write the set expression for the desired results of the Web search query for sites pertaining to dogs that are
not retrievers (Exercise 31, Section 1.1). Assume that D = set of dog pages, R = set of retriever pages.
60. Write the set expression for the desired results of the Web search query for sites pertaining to oil paintings
by Van Gogh or Rembrandt but not Vermeer (Exercise 32, Section 1.1). Assume that O = set of oil painting pages, G = set of Van Gogh pages, R = set of Rembrandt pages, V = set of Vermeer pages.
61. Write the set expression for the desired results of the Web search query for sites pertaining to novels or
plays about AIDS (Exercise 33, Section 1.1). Assume that N = set of novel pages, P = set of play pages,
A = set of AIDS pages.
62. Write the set expression for the desired results of the Web search query for sites pertaining to coastal
wetlands in Louisiana but not in Alabama (Exercise 34, Section 1.1). Assume that C = set of coastal
wetlands pages, L = set of Louisiana pages, A = set of Alabama pages.
63. Which of the following statements are true for all sets A, B, and C?
a. A c A = A
d. (A′)′ = A
b. B d B = B
e. A − B = (B − A)′
c. (A d B)′ = A′ d B′
f. (A − B) d (B − A) = [
64. Which of the following statements are true for all sets A, B, and C?
a. If A d B = [, then A ( B.
d. [ d {[} = [
b. B × A = A × B
e. (A − B) c (B − C ) = A − C
c. [ × A = [
f. (A − C ) d (A − B) = A − (B c C )