Example 2

We will prove the following argument:

Again, we begin with our conclusion, and we work backwards. Our conclusion, "D", a simple sentence letter, is the consequent of the condition in the second premise. So we need to derive it from the second premise, along with something else. But what is that something else? One possibility is that we have the antecedent of the second premise, namely "(B v C)" as a separate line in our proof. How can you get that? You can use mp from the first and third premises. But what other option do we have? Notice that our first two premises meet the conditions for the application of the rule hs. If we use that, we can derive "(A ⊃ D)". Then we can use modus ponens to derive D. So we've outlined two ways to do this proof.

Write out the full proof on your own.

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