Answer to Question #304232 in Discrete Mathematics for Sinatra

Question

Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Find

a. (A ∪ B) ∩ C.

b. (A ∩ B) ∪ C.

c. (A ∪ B) ∩ (A ∪ C).

Answer 1

a) we define (A ∪ B) ={ 0,1,2,3,4,5,6,8,10}

Hence (A ∪ B) ∩ C. = {4,5,6,8,10}

b)we define (A ∩ B ) = {2,4,6}

Hence (A ∩ B) ∪ C = {2,4,5,6,7,8,9,10}

c) we define (A ∪ B) = { 0,1,2,3,4,5,6,8,10}

we define (A ∪ C) = {0,2,4,5,6,7,8,9,10}

Hence (A ∪ B) ∩ (A ∪ C) = {0,2,4,5,6,8,10}