Question

Show that the argument form with premises\(p1,p2,...pn\)and conclusion\(q \to r\)is valid if the argument form with premises\(p1,p2,...pn,q,\)and conclusion\(r\)is valid.

Short answer

It has been proved that the argument form with premises \(p1,p2,...pn\)and conclusion \(q \to r\)is valid if the argument form with premises \(p1,p2,...pn,q,\) and conclusion\(r\) is valid.

Step-by-step solution

Definition of Argument    

Theargument is a collection of propositions that have premises and a conclusion.

To show the argument form with premises \(p1,p2,...pn\) and conclusion \(q \to r\)is valid if the argument form with premises \(p1,p2,...pn,q,\) and conclusion\(r\) is valid.

Suppose \(q\) is false.

So, \(q \to r\) is true and concluded\(q \to r\).

Now, assume that \(q\) is true.

The argument form with premises\(p1,p2,...pn\)and conclusion\(q \to r\)is valid.

Hence, the conditional statement\(q \to r\)is true.

Therefore, it has been proved that the argument form with premises \(p1,p2,...pn\) and conclusion \(q \to r\)is valid if the argument form with premises \(p1,p2,...pn,q,\) and conclusion \(r\) is valid.