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28 March, 18:58

Let A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, and C = {5, 6, 7, 8}. Find each of the following sets. (Enter your answers in set-roster notation.) (a) A Δ B (b) B Δ C (c) A Δ C (d) (A Δ B) Δ C

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  1. 28 March, 22:15
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    (a) {1, 2, 5, 6}

    (b) {3, 4, 7, 8}

    (c) {1, 2, 3, 4, 5, 6, 7, 8}

    (d) {1, 2, 7, 8}

    Step-by-step explanation:

    Given sets,

    A = {1, 2, 3, 4}, B = {3, 4, 5, 6} and C = {5, 6, 7, 8},

    (a) Since, A Δ B = (A/B) ∪ (B/A) = all elements of A/B and B/A

    ∵ A/B = elements of set A which are not in B

    = {1, 2}

    And, B/A = {5, 6}

    So, A Δ B = {1, 2, 5, 6}

    (b) B/C = {3, 4},

    C/B = {7, 8}

    ⇒ B Δ C = (B/C) ∪ (C/B) = {3, 4, 7, 8}

    (c) A/C = {1, 2, 3, 4},

    C/A = {5, 6, 7, 8},

    ⇒ A Δ C = (A/C) ∪ (C/A) = {1, 2, 3, 4, 5, 6, 7, 8}

    (d) (A Δ B) / C = {1, 2}

    C / (A Δ B) = {7, 8}

    A Δ C = ((A Δ B) / C) ∪ (C / (A Δ B)) = {1, 2, 7, 8}
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