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2 January, 06:25

Given A={x ∈ Z : x is even}, B={x ∈ Z : x is prime number}, C={x ∈ Z : x is odd}, and D={5, 7, 8, 12, 13, 15}.

(a) Find D - (A ∪ B)

(b) Find D - (A ∪ C)

(c) Find D - (A ∩ B)

(d) Are A and B Disjoint? Explain.

(e) Are A and C Disjoint? Explain

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Answers (1)
  1. 2 January, 08:20
    0
    a) {15}

    b) { }

    c) D or {5, 7, 8, 12, 13, 15}

    d) no

    e) yes

    Step-by-step explanation:

    a) AUB: even or prime

    D - (AUB) = {15}

    b) AUC: even or odd; basically all integers

    D - (AUC) = { }

    c) A∩B : even and prime, that's only 2

    D - (A∩B) = {5, 7, 8, 12, 13, 15} = D

    d) A and B, both contain 2

    Not disjoint

    e) A and C are disjoint because no number can be both, even and odd
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