Rules of replacement question.

Hi guys I am taking up discrete math today.
I am kinda confuse with the rules of replacement.
My question is how should I know whether in the second procdure that I will use Idempotence or other rules in it.

Thanks guys...

And merry christmas to all of you.

happy new year...!

I'am also doing discrete math since one year more or less.
i have been looking at differents books talking about discrete math and i must say that this appelation seems to carry an amazing lot of topics!
So you should had telling us what you were talking of.
You would probably had more reply!

see you
by