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' ∪ C) ∩ B'

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' ∪ C) ∩ B'

A' ∪ C = { r, t, v, x, z } ∪ { v, w, x, y, z } = { r, t, v, w, x, y, z }

(A' ∪ C) ∩ B' = { r, t, v, w, x, y, z } ∩ { r, t, u, v, w, x } = { r, t, v, w, x }

Answer: (A' ∪ C) ∩ B' = { r, t, v, w, x }

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