Damn, this is pretty dense stuff.

Was Boolean algebra relatively difficult for you when you first learned it?

It was a while back when I learned it, but with time, it becomes intuitive. You'll get the hang of it: It gets messy: that's part of the confusing part!

messy as in lots of difficult to read notation? cause I can definitely see that.

though I suppose the notation would become intuitive

Yes, the notation will become quite familiar. But initially, it is really like learning a new language, with the need to keep translating to what is more familiar. But once you learn the "language", it will read much more smoothly.

I am a bit confused still about /equiv. What is the truth table for it?

Other than that I think I understand everything now except are still steps left for the proof

p \equiv q < - > p if and only if q <---> see the truth table here. URL: (wolframalpha.com/input/?i=p+iff+q)

It means the same as [( p --> q) AND ( q --> p ) ]

feel free to accept my answer, when you're ready. ;-) Even if you accept now, I will still be available if you "ping" me: @amwhy, or commenting below my answer --> I get notified.

Alright, thanks alot for your help

You're welcome!

I think I need a break for now. I will accept your answer. Technically I feel that its not complete because it doesn't show the final steps of the proof, but you have taught me so much other stuff that I think you more than deserve the accept.

Thanks...I'll be around!

Cool. Now I kinda feel bad for nitpicking. It really means a lot to me that you took the time to help. Take care.

Do not worry! I didn't take offense!. Good luck!