Answer to Question #264446 in Discrete Mathematics for nyokie

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 }. (2 pts each)

Find 

a) A ∩ B ∩ C

b) A ∪ B ∪ C

c) ( A ∪ B) ∩ C

d) ( A ∩ B) ∪ C

Answer 1

Solution:

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

a) A ∩ B ∩ C = {4, 6}

b) A ∪ B ∪ C = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

c) ( A ∪ B) ∩ C = {0, 1, 2, 3, 4, 5, 6, 8, 10} ∩ {4,5,6,7,8,9,10} = {4, 5, 6, 7, 8, 10}

d) ( A ∩ B) ∪ C ={0, 2, 4, 6} ∪ {4,5,6,7,8,9,10} = {0, 2, 4, 5, 6, 7, 8, 9, 10}