Answer
The argument
\[\frac{\begin{align}
& p\to q \\
& q\to r \\
\end{align}}{\therefore \underline{p\to r}}\]
Is called direct reasoning and is valid because\[\left[ \left( p\to q \right)\wedge \left( q\to r \right) \right]\to \left( p\to r \right)\] is a tautology.
