if x->t,x->t and x-> z what type of argument typeis this in logics?

Answer 1

I'm going to guess that you meant to ask:

"if x->t and t->z, then x-> z."

I.e. The statements "if x, then t" and "if t, then z" imply that "if x, then z".

This is a logical rule of inference called "hypothetical syllogism".

A classic example of it is:

Socrates is a philosopher. All philosophers are human. Therefore, Socrates is human.

Hope that's what you wanted.