Question

let

U = {a, b, c, d, e, f, g, h, i, j, k}
A = {a, c, d, f, g, i}
B = {b, c, d, f, g}
C = {a, b, f, i, j}

Determine the following.
A ∪ (C′ ∪ B′)

Answer 1

C' consists of all elements in the universal set, U, that are not in C; similarly for B', thus

C' = {c, d, e, g, h, k}
B' = {a, e, h, i, j, k}

the union of set C' with B' consists of all elements in either C', or B' or both sets

C' U B' = {a, c, d, c, g, h, i, j, k}

the the union of A with C' U B again consists of al the elements in either set or both sets

A U (C' U B') = {a, c, d, f, g, h, i, j, k}