Answer
The statement:“Any argument whose premises are and is valid regardless of the conclusion” is false.
Work Step by Step
It is possible for an invalid argument to have premises are \[p\to q\]and \[q\to r\].
For example –
The argument
If I’m tired, I’m edgy.
If I’m edgy, I’m nasty.
\[\therefore \]If I’m nasty, I’m tired.
Use a letter to represent each simple statement in the argument.
p: I’m tired.
q: I’m edgy.
r: I’m nasty.
Express the premises and conclusion symbolically.
\[\frac{\begin{align}
& p\to q \\
& q\to r \\
\end{align}}{\therefore r\to p}\ \ \ \ \ \frac{\begin{align}
& \text{If Im tired, Im edgy}\text{.} \\
& \text{If Im edgy, Im nasty}\text{.} \\
\end{align}}{\therefore \text{If Im nasty, Im tired}.}\]
This symbolic form of argument follows the standard form, invalid argument, and Misuse of Transitive Reasoning.
\[\frac{\begin{align}
& p\to q \\
& q\to r \\
\end{align}}{\therefore r\to p}\]
