Here is an argument that I adapted from John Heil, First-Order Logic: A Concise Introduction (Boston: Jones and Bartlett Publishers, 1994). (Prof. Heil teaches at Davidson College.) It can be done without IP but it is a lot easier with IP.

1. A É (B Ú C)

2. ~A É C

3. ~B      /\ C

The first thing you do is assume the negation of the conclusion as line 4.

Then your objective is to derive a contradiction.

You can use Indirect Proof on any of the valid arguments we have studied thus far. For instance, here is the first one from Exercise 13:

1. P É Q

2. Q É R

3. P

4. ~R Ú S     /\ S

(Of course, in this case there is nothing to be gained by doing an IP. It was easier to do it as we did in Exercise 13 without IP. But still one could do an IP at any time. Obviously, one saves IP for those times when one is confident that the argument is valid and yet cannot figure out how to do a direct proof.)

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Copyright © 1999, Michael Eldridge