Example 1

We will prove the following argument:

Before we construct a proof, we attempt to develop a strategy. We can't simply blindly apply the rules that occur to us, since a mere application of the rules doesn't guarantee that we will arrive at a proof of our conclusion.  So we begin by asking ourselves: What is the conclusion, and where does the conclusion occur as part of the premises?  We note that our conclusion is "~S", which doesn't occur anywhere as part of a premise. However, "S" is the antecedent of a conditional, the conditional "(S � T)" which is the right disjunct of the first premise. Suppose we could derive "(S � T)" by itself. What would it take to infer ~S? Suppose we had ~T. Then we get ~S by Modus Tollens. But we have ~T as a premise! So we're home free!

Using the information provided, construct the proof on your own. When you're done, your proof should look something like this one.

close