if the truth value of p is T, what is the truth value of r?

according to the law of syllogisms, we have that if p is true and q is true then r is also true. we are given that:
[tex]p\rightarrow q[/tex]That means that when p is true q is also true.
We are also given that:
[tex]q\rightarrow r[/tex]Since we already established that q is true this means that r is also true. therefore, if p is true r is true.