Question

Prove that 1. AU(BUC)=(AUB)UC

Answer 1

You can see like this, there are 3 sets A, B & C, and they are joint sets.

figure must be like 3 circles intersecting each other.

AUBUC = AUBUC (this is final answer)
now you are making this like : AU(BUC) = (AUB)UC ; this is equal AUBUC

Take this equation then maybe you will understand, If Set A = {1}, Set B = {2} and Set C = {3}
AUBUC = AU(BUC) = (AUB)UC
1+2+3 = 1+(2+3) = (1+2)+3
this all be same bcoz and always be 6 = AUBUC