Mathematical Proof Strategy

Mathematical Proof Strategy

1. CONTRAPOSITIVE

   • PROPOSITION : P → Q is logically equivalent to a ~Q → ~P
   • EXAMPLE
   • OUTLINE
   • Alternative to direct proof

2. CONTRADICTION

   • Assume statement to be proven is false, then show that assumption leads to nonsense
     • To make a statement false, only negate Q 
     • Not limited to proving just conditional statements
   • PROPOSITION : P is logically equivalent to (~P) → (C ^ ~C)
   • OUTLINE
   • EXAMPLE

3. MATHEMATICAL INDUCTION

   • Used when we have a set of statements S1, S2, S3, ..., Sn, ..., and we need to prove that they are all true
   • OUTLINE
   • EXAMPLE

4. DIRECT PROOF

   • OUTLINE
   • PROPOSITION : If P, then Q
   • A simple way to prove theorems or propositions that have the form of conditional statements
   • EXAMPLE

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