Tutorial: Getting Started

This tutorial includes ten relatively short examples of proofs that illustrate most of the features of DC Proof. In addition, there are 20 exercises with hints and full solutions provided here. They can also be found in the DC Proof / Samples directory.

To Students:

It is recommended that you work through each example in order, recreating each proof on the DC Proof main screen as you go . While some examples may seem trivial, there are important lessons in each one. As you read through this tutorial, all menu options and controls on the main screen remain fully functional.

To Instructors:

Examples 1 through 4 introduce the concept of a formal proof using propositional logic. Examples 5 through 7 introduce predicate logic and some elements of algebra. Example 8 introduces fundamental concepts of modern set theory. Examples 9 and 10 introduce elementary number theory and proof by induction.

Methods of Proof Used

Tutorial Example	Direct Proof	Proof by Contradiction	Proof by Cases	Quantifiers	Proof by Induction	Set Theory	Number Theory
1. The Commutativity of AND	x
2. The Transitivity of IMPLIES	x
3. The Commutativity of OR		x
4. The Distributivity of AND over OR	x		x
5. The Transitivity of Equality	x			x		x
6. The Composition of Functions	x			x		x
7. The Barber Paradox		x		x
8. The Paradox of the Universal Set		x		x		x
9. The Set of Natural Numbers	x			x			x
10. Proof by Induction		x		x	x	x	x

See the DC Proof/Samples directory for all Tutorial Examples, Exercise Solutions, Hints and more in the DC Proof format.

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