HELP! MATH QUESTION?

Question

1) Given the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and sets A = {1, 3, 4, 8}, B = {1, 2, 3, 5, 6}, C = {1, 2, 10}, and D = {2, 4, 7, 9}, answer the following: 
a) What is B∪(C∪D)? 
b) What is A∩B? 
c) Whatis A′∩(B∪D)?

Answer 1

The sets are U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 4, 8}, B = {1, 2, 3, 5, 6} C = {1, 2, 10} and D = {2, 4, 7, 9}.

(a).

Find BU(CUD):

CUD = {1, 2, 10} U {2, 4, 7, 9} = {1, 2, 4, 7, 9,10}.

BU(CUD) = {1, 2, 3, 5, 6} U {1, 2, 4, 7, 9,10} = {1, 2, 3, 4, 5, 6, 7, 9,10}.

(b).

A∩B = {1, 3, 4, 8} ∩ {1, 2, 3, 5, 6} = {1, 3}.

(c).

Find A'∩(BUD):

BUD = {1, 2, 3, 5, 6} U {2, 4, 7, 9} = {1, 2, 3, 4, 5, 6, 7, 9}.

A' = U - A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} - {1, 3, 4, 8}, = {2, 5, 6, 7, 9, 10}.

A'∩(BUD) = {2, 5, 6, 7, 9, 10} ∩ {1, 2, 3, 4, 5, 6, 7, 9} = {2, 5, 6, 7, 9}.