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8 March, 19:57

LetA, B, C and D be the following sets:

A={red, blue, green, purple}

B={red, red, green}

C={red,{green}, red,{red, green},{green, green, red}}

D={blue, blue, blue, green, green, purple}

Let the universal set for A, B, C, D be defined by:

U={red, blue, purple, green}⋃P ({red, blue, purple, green}) Provide the answer to the following quesitons about the above sets:

(A) : Is B ∈ A?

(B) : Is B ∈ C?

(C) : Is B ∈ P (C) ?

(D) What is |A|?

(E) What is |C|?

(F) What is |D|?

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Answers (1)
  1. 8 March, 20:14
    0
    (a) No

    (b) Yes

    (c) No

    (d) 4

    (e) 3

    (f) 3

    Step-by-step explanation:

    A = {red, blue, green, purple}

    B = {red, red, green}

    C = {red,{green}, red,{red, green},{green, green, red}}

    D = {blue, blue, blue, green, green, purple}

    U = {red, blue, purple, green}∪ P ({red, blue, purple, green})

    By removing duplicate elements, the sets become

    A = {red, blue, green, purple}

    B = {red, green}

    C = {red, {green}, {red, green}}

    D = {blue, green, purple}

    U = {red, blue, purple, green} ∪ P ({red, blue, purple, green})

    (a) B ∉ A because B is a set while A contains elements that are not sets, even thought the elements of B are also in A. In fact, B is a subset of A.

    (b) B ∈ C because {red, green} is a member of C.

    (c) P (C) is the power set of C, the set of all subsets of C. The power set of C is

    P (C) = {{}, {red}, {{green}}, {{red, green}}, {red, {green}}, {red, {red, green}}, {{green}, {red, green}}, {red, {green}, {red, green}}}

    It is seen that B ∉ P (C).

    (d) |A| is the cardinality of A or the number of distinct members of A.

    Therefore, |A| = 4

    (e) |C| = 3 (Note that the elements in the member set are not counted)

    (f) |D| = 3
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