Question

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')

Answer 1

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.