derivations

Example of a Harder Propositional Proof: One of De Morgan's Laws

10/23/06

Example

Example of a Harder Propositional Proof

2/27/06

Example

2013

Skills to be acquired:

Learning the Rules Or Elimination and the Introduction of the Biconditional.

The Tutorial:

Or Elimination, in the guise of Dilemma, also is a form of inference dating from antiquity.

The core idea of it that if a conclusion follows from both disjuncts of a disjunction, then the conclusion follows full stop. As an example in English, if either I am going to eat an ice-cream or I am going to eat some cake, and if I eat ice-cream I break my diet, and if I eat cake I break my diet, then ... I break my diet.

Quiz 6 Applet

This contains an applet, so it will be slow loading and likely it will ask you about security.

Reductio ad Absurdum

2/24/06

Absurd Introduction and Simple Reductio

2013

Skills to be acquired:

Learning reductio proof, both as plain Negation Introduction and via (double) Negation Elimination (to prove some formulas that do not have negation as their main connective).

The Tutorial:

Reductio ad Absurdum is the second of the classical forms of inference.

9/12/06

Conditional Proof

This video shows the techniques for Conditional Proof using the downloadable application Deriver. But the techniques are exactly the same for the Proof applet running in a web page. So, the video may look slightly different to what you are looking at, but the underlying principles and approach are the same.

2013

Skills to be acquired:

Learning conditional proof.

The Tutorial:

The four remaining propositional rules of inference are slightly more difficult than the ones that we have met before. They are slightly more difficult in that they require you to make new assumptions, and the correct new assumptions at that. However they follow a similar pattern to each other so mastery of one should lead to mastery of the others.

Two of them are classical forms of inference, dating back thousands of years-- we will look at these first.

12/22/05

Introduction to Tactics

This video is set in the context of the downloadable program, but it applies equally well in the setting of a proof applet.