Show that the argument form with premises p lambda t rightar

Show that the argument form with premises (p lambda t) rightarrow (r v s), q rightarrow (u lambda t), u rightarrow p, and s and conclusion q rightarrow r is valid by first using Exercise 11 and then using rules of inference from Table 1.

Solution

We want to show that the conclusion r follows from the five premises (pt)(rs), q(ut), up, ¬s, and q. From q and q(ut) we get ut by modus ponens. From there we get both u and t by simplification(and the commutative law).From u and up we get p by modus ponens. From p and t we get pt by conjunction. From that and (pt)(rs) we get rs by modus ponens. From that and ¬s we finally get r by disjunctive syllogism.