Sets and Set Operations

4.  Let A = {a, {a}, {{a}}}
           B = {ø, {a}, {a, {a}}}
           C = {a}
Be subsets of S = {ø, a, {a}, {{a}}, {a, {a}}}.  Find
a)  A    C
b)  B    C'
c)  A    B
d)  ø     B
e)  (B    C)      A
f)  A'      B
g)  {ø}      B

5.  Let A = {x | x is the name of a former president of the US}
           B = {Adams, Hamilton, Jefferson, Grant}
           C = {x | x is the name of a state}

Find:
a)  A    B
b)  A    C
c)  B     C

6.  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 computer science majors
b)  set of all male students who are not physics majors
c)  set of all science majors who are not computer science majors
d)  set of all students who are female or science majors

7.  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.  Assume that O = set of oil painting pages, G = set of Van Gogh pages, R = set of Rembrandt pages, V = set of Vermeer pages.

See attached file for full problem description.

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4. Let A = {a, {a}, {{a}}}

B = {Ñˆ, {a}, {a, {a}}}

C = {a}

Be subsets of S = {Ñˆ, a, {a}, {{a}}, {a, {a}}}. Find

a) A C

b) B Câ€™

c) A B

d) Ñˆ B

e) (B C) A

f) Aâ€™ B

g) {Ñˆ} B

5. Let A = {x | x is the name of a former president of the US}

B = {Adams, Hamilton, Jefferson, Grant}

C = {x | x is the name of a state}

Find:

a) A B

b) A C

c) B C

6. 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 computer science majors

b) set of all male students who are not physics majors

c) set of all science majors who are not computer science majors

d) set of all students who are female or science majors

7. 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. Assume that O = set of oil painting pages, G = set of Van
Gogh pages, R = set of Rembrandt pages, V = set of Vermeer pages.

Sets and Set Operations are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.