About the first order logic (valid, Unsatisfiable, Syntactically wrong)

I am in trouble , I searched a lot about how to solve this kind of questions but I did not get any answers.

I understand how can I know when the sentences is valid and Unsatisfiable in propositional logic, but in FOL I can't.

Can someone help me how can I solve this kind of questions? Because it comes always in the past exams in AI.

Let us have the following:

1- ¬(Speed(Processor(MyPC))=Speed(Processor(MyPC)))
2- ¬ ∃ x ( Speed(x) = Speed(MyPC) )
3- Speed(MyPC)=MyPC
4- ∀ y ∃ x (Speed(x) ∧ Speed(y))= Speed(MyPC)

Note :

MyPC:
a constant symbols that represents my PC.

Speed(x):
a function symbol that refers to speed of x

The answer for 1 is Syntactically wrong
2 is Unsatisfiable
3 is Neither valid nor unsatisfiable
4 is Syntactically wrong

• Welcome to Computer Science! The title you have chosen is not well suited to representing your question. Please take some time to improve it; we have collected some advice here. Thank you!
– Raphael
Jan 1 '17 at 20:04

3 is not universally true for every function Speed and every argument MyPC. For instance interpret MyPC as the natural $0$, and Speed as the successor function to obtain $\mathsf{succ}(0)=0$ which is false. Hence the formula is not valid. However, it is satisfiable: now interpret MyPC as zero and Speed as the identity function to obtain $\mathsf{id}(0)=0$ which is true. The formula has a model and a countermodel: satisfiable and invalid.