Question

Let A = {a, b, c}, B = {b, c, d}, and C = {b, c, e}. (a) Find A ∪ (B ∩ C), (A ∪ B) ∩ C, and (A ∪ B) ∩ (A ∪ C). (Enter your answer in set-roster notation.)

Answer 1

a. A U (B n C)
B n C = {b,c}
A = {a,b,c}
A U (B n C) = {a,b,c} U {b,c} = {a,b,c}

b. A U B = {a,b,c} U {b,c,d} = {a,b,c,d}

c. (A U B) n (A U C)

A U B= {a,b,c,d}
A U C= {a,b,c,e}

(A U B) n ( A U C)

➡️ {a,b,c,d} n {a,b,c,e}

➡️ {a,b,c}

Answer 2

(B n C) = {b,c}

A = {a,b,c}

B= {b,c,d}

C= {b,c,e}

A u (B n C) = {a,b,c}

(A u B) = {a,b,c,d}

(A u B) n C = {b,c}

(A u C) = {a,b,c,e}

(A u B) n (A u C) = {a,b,c}