Use the following set definitions to specify each set in roster notation. Except where noted, express elements of Cartesian products as strings. A = {a} B = {b, c} C = {a, b, d}

(a) A * (B ∪ C) Solution {aa, ab, ac, ad}

(b) A * (B ∩ C)

(c) (A * B) ∪ (A * C)

(d) (A * B) ∩ (A * C)

Step-by-step explanation:

Given the set notations A = {a} B = {b, c} C = {a, b, d}

BUC = {a, b, c, d}

B∩C = {b}

a) A * (BUC) = {aa, ab, ac, ad}

b) A * (B ∩ C) = {ab}

c) (A * B) ∪ (A * C)

A * B = {ab, ac} and A * C = {aa, ab, ad}

(A * B) ∪ (A * C) = {aa, ab, ac, ad}

d) For (A * B) ∩ (A * C)

(A * B) ∩ (A * C) = {ab}

Note that the union (U) of two sets is the combination of all the elements in both sets while the intersection (∩) of two sets is the common elements that are found in both sets.

The Cartesian product of two sets is derived by mapping each of the element in the first set with all the element in the other set. It is denoted by the multiplication sign.