Conditional Proof or Deduction Theorem Examples

In this class, We discuss Conditional Proof or Deduction Theorem Examples.

The reader should have prior knowledge of Showing Valid Inference Examples 1. Click here.

Conditional proof rule:

If we can derive S from R and some other premises, then we can derive R -> S from the set of premises.

Example:

Show that r -> s can be derived from the premises p -> (q -> s), (¬r ∨ p), q

From the conditional proof, we can derive s from the set of premises p -> (q -> s), (¬r ∨ p), q and r

Solution:

The diagram below shows the derivation