Question

Given, A={1,2,3,4,5} B={3,4,5,6} & C={5,6,7,8}, show that AU(BUC)=(AUB)UC

Answer 1

Given data:
A={1,2,3,4,5}
B={3,4,5,6}
C={5,6,7,8}
Required to show:
AU(BUC)=(AUB)UC

SOLUTION:-
1st we find AU(BUC).
So
AU(BUC)
={1,2,3,4,5}U({3,4,5,6}U{5,6,7,8})
={1,2,3,4,5}U({3,4,5,6,7,8})
={1,2,3,4,5}U{3,4,5,6,7,8}
={1,2,3,4,5,6,7,8}-----------------(1)

Now we find (AUB)UC
So
(AUB)UC
=({1,2,3,4,5}U{3,4,5,6})U{5,6,7,8}
=({1,2,3,4,5,6})U{5,6,7,8}
={1,2,3,4,5,6}U{5,6,7,8}
={1,2,3,4,5,6,7,8}---------------------(2)

Comparing equations (1) and (2) It is proved that AU(BUC)=(AUB)UC