Proof by Contradiction

One strategy for proving the validity of an argument is Proof by Contradiction which is based on the Reductio ad Absurdum (Latin for "reduction to the absurd") argument.

In this type of proof, we usually assume the negation of the conclusion. We use this assumption together with the other premises to derive a result. This result is either already known to be false or can be shown to be false. Since the result cannot both be true and false then it follows that the initial assumption must be false i.e. the conclusion holds.

Let's use propositional logic and the Proof by Contradiction approach to prove the following argument.

Either Veronica is not from Riverdale or Dilton is not smart.
Dilton is smart.
If the Lodges did not move then Veronica is from Riverdale.
Therefore the Lodges moved.

Let R be the proposition "Veronica is from Riverdale."
Let S be the proposition "Dilton is smart."
Let M be the proposition "The Lodges moved."