How | To Prove It: A Structured Approach
Show the goal holds in all possible scenarios. 3. The "Scratch Work" Process
The choice of technique is dictated by the of your "Goal" statement. Statement Type Example Structure Common Approach Conditional ( P→Qcap P right arrow cap Q Suppose-Until: Assume is true and work toward Universal ( Arbitrary : Let be an arbitrary object and prove Existential ( "There exists an such that..." Example: Find or construct a specific that works. Disjunction ( How to Prove It: A Structured Approach
Velleman emphasizes a systematic two-column style approach for organizing thoughts before writing the final proof: HOW TO PROVE IT: A Structured Approach, Second Edition Show the goal holds in all possible scenarios
Velleman compares writing proofs to . Just as a program uses nested blocks (like if-else or do-while ), a proof is built by nesting logical structures based on the form of the statement being proven. 1. Mastering the Logic Fundamentals 1. Mastering the Logic Fundamentals
