Features

• DC Proof is a free, downloadable, PC-based educational software program that can be used to learn basic proof-writing skills
   
• Recommended for use by...
  • undergraduates in transition to proof-based mathematics
  • teachers in training
  • advanced high school students
     
• Simplified rules and axioms of formal logic and set theory
  • more like the implicit rules of inference students will find in mathematics textbooks
  • based on the simplifying assumption that every branch of mathematics is based on the existence of one or more underlying sets (e.g. the set of integers in number theory)
  • neatly avoids a number of prickly philosophical issues
     
• Convenient, pull-down menus enables you to apply any of the rules and axioms of logic, set theory and number theory with the click of a mouse
   

   Fig. 1. Menu of the rules of Logic.
 

• See additional screen shots
   
• User comments and meaningful variable names (of unlimited length) facilitate both the reading and writing of proofs

Example

Suppose that it is sunny if any only if it is it not cloudy. 

1     Sunny <=> ~Cloudy
      Premise 

Fig. 2 User comment in blue. Line number and logical statement in black. Rule used in gray.
 

• Color-coded variables that indicate at a glance when generalizations can be made

• Multi-level views of proofs that hide or reveal details as required ─ indispensible for writing longer proofs!

 
Symbolic Logic and The Basic Methods of Proof

• DC Proof includes an interactive tutorial that introduces symbolic logic and the basic methods of proof using worked examples and exercises with hints and full solutions
   
  • Topics in symbolic logic include:
    • Logical propositions and predicates
    • Logical operators
    • Quantifiers ─ free and bound variables
       
  • Methods of proof include:
    • Direct proof
    • Indirect proof
      • Proof by contradiction
      • Proof by contrapositive
    • Proof by cases
    • Proof of biconditionals
    • Proof by induction
    • Use of the formal axioms and definitions
      • Set theory
      • Elementary number theory

  
  Examples of the Methods of Proof

  Tutorial Example	Direct Proof	Proof by Contradiction	Proof by Contrapositive	Proof by Cases	Proof of Biconditionals	Manipulating 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 (by contradiction)		x
  4. The Commutativity of OR (by contrapositive)			x
  5. Proving a Biconditional	x	x			x
  6. The Distributivity of AND over OR  (Part 1)	x			x
  7. The Transitivity of Equality	x					x
  8. The Composition of Functions	x					x
  9. The Barber Paradox		x				x		x
  10. The Paradox of the Universal Set		x				x		x
  11. The Uniqueness of the Empty Set	x	x	x		x	x		x
  12. 1+1=2, 2+2=4	x					x		x	x
  13. No Number its own Successor		x				x	x	x	x

  Fig. 3 Table of methods of proof used in tutorial