Indirect Method of Proof Examples

In this class, We discuss the Indirect Method of Proof Examples.

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

Indirect method of proof:

Show that r follows from the set of premises p -> q, q -> r, ¬(p ∧ r), (p ∨ r).

In the indirect method, we assume the conclusion is false.

So, negate the conclusion to make it true.

Add the negation of the conclusion to the premises, and we show false from the premises and added conclusion.

When we show false meaning, our assumption that the conclusion is false is wrong.

So, the conclusion is true.

We need to show false from the premises p -> q, q -> r, ¬(p ∧ r), (p ∨ r), and ¬r.

The below diagram shows the derivation.