Given the following sets, for each set operation provide the elements of the resulting set in set notation or using a well-known set, i. e. N, the set of natural numbers

Z, the set of all integers

Z+, the set of all positive integers

Z-, the set of all negative integers

A, the set of all integers evenly divisible by 3

B={4, 5, 9, 10 }

C={12,4,11,14)

D={3,6,9}

E = {4,6, 16}

a. B U C

b. A ⋂ D

c. A⋂C

d. (B+D) + E

e. AUE

f. E-D

g. D-E

h. (Z - Z+) - Z

Check the explanation

Explanation:

Z - > the set of all integers

Z + - > the set of all positive integers

Z - - > the set of all negative integers

A - > the set of all integers evenly divisible by 3

B - > {4,5,9,10}

C - > {2,4,11,14}

D - > {3,6,9}

E - > {4,6,16}

Questions:

a. B U C

Answer: {2,4,5,9,10,11,14}

b. A ∩ D

Answer: {3,6,9}

c. A ∩ C

Answer: {} or null set or ∅

d. (B⊕D) ⊕ E

Answer:

A ⊕ B denotes the Symmetric difference between A and B.

The result of the operation is the elements that in either of the sets but not in their intersection.

For the question

B - > {4,5,9,10}

D - > {3,6,9}

Elements that are not in the intersection of the two sets that are.

{3,4,5,6,10} here 9 is omitted because it is present in both the sets.

{3,4,5,6,10} ⊕ E

E - > {4,6,16}

The result will be {3,5,19,16} here 4,6 are the intersection of both sets.

So the answer is {3,5,19,16}

e. A U D

Answer: the set of all integers divisible evenly by 3.

f. E - D

Answer: {4,16}

g. D - E

Answer: {3,9}

h. (Z - Z+) - Z-

Answer: (Z - Z+) means remove all the integers from Z that are present in Z + which results all the negative integers and 0.

({0, Z-} - Z-) results in {0}.

So the final answer is {0}