Trying to go through Tom Apostle text on Calculus. There is an exercise about proving the associative law for sets:

So, (A U B) U C = A U (B U C)

So, if we assume x to be an element in set in left hand side, than we can say x belongs at least to either A, B or C which in turn means that x is also an element in set in right hand side and then we can say that the LHS and RHS are subsets of each other...

Is this a valid proof? I am never sure with these. It is really tricky to prove such ideas that we take for granted in every day life!

Anyway, I would be really grateful for any help you can give this old man.

/Luca