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28 April, 11:03

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

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Answers (1)
  1. 28 April, 14:15
    0
    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}
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