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23 November, 20:49

Let U = {q, r, s, t, u, v, w, x, y, z}

A = {q, s, u, w, y}

B = {q, s, y, z}

C = {v, w, x, y, z}

Determine the following.

(A ∩ B') ∪ (B ∩ A')

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Answers (1)
  1. 23 November, 22:48
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    U = { q, r, s, t, u, v, w, x, y, z }

    A = { q, s, u, w, y } → A' = { r, t, v, x, z }

    B = { q, s, y, z } → B' = { r, t, u, v, w, x }

    C = { v, w, x, y, z }

    A ∩ B' = { q, s, u, w, y } ∩ { r, t, u, v, w, x } = { u, w }

    B ∩ A' = { q, s, y, z } ∩ { r, t, v, x, z } = { z }

    (A ∩ B') ∪ (B ∩ A') = { u, w } ∪ { z } = { u, w, z }

    Answer: (A ∩ B') ∪ (B ∩ A') = { u, w, z }

    A' = U - A, B' = U - B

    The union A ∪ B, is the set of all things that are members of either A or B.

    The intersection A ∩ B, is the set of all things that are members of both A and B.
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