What are the steps for using natural deduction in logic?

[Firepanda]

Logic: Natural Deduction

Can anyone lead me off here? I've broken down the three premises using 'for all' elimination, now I need to start a subderivation with an assumption, but I'm not sure what!

Right now I'm unsure of the strategy I need to use to get to the conclusion, what do I want to be left with to manipulate into the conclusion?

Would be grateful for any help!

A list of the inference rules I have learned so far for Natural deduction can be found HERE

 

[Firepanda]

I've reduced the problem to the above, if I can prove the above then I can prove the whole thing! (I think..!)

Any help on this one? Thanks :)

 

[Firepanda]

Apparantly my above inference isn't valid so I cannot proceed with this method

My initial assumption is assuming P(a,b) & P(b,a)

Really stuck, would appreciate help!

Thanks