Mathematical Proof Strategy

CONTRAPOSITIVE
1. PROPOSITION : P → Q is logically equivalent to a ~Q → ~P
2. EXAMPLE
3. OUTLINE
4. Alternative to direct proof
CONTRADICTION
1. Assume statement to be proven is false, then show that assumption leads to nonsense
  1. To make a statement false, only negate Q 
  2. Not limited to proving just conditional statements
2. PROPOSITION : P is logically equivalent to (~P) → (C ^ ~C)
3. OUTLINE
4. EXAMPLE
MATHEMATICAL INDUCTION
1. Used when we have a set of statements S1, S2, S3, ..., Sn, ..., and we need to prove that they are all true
2. OUTLINE
3. EXAMPLE
DIRECT PROOF
1. OUTLINE
2. PROPOSITION : If P, then Q
3. A simple way to prove theorems or propositions that have the form of conditional statements
4. EXAMPLE

Resource summary

	Created by Naimi Syahira over 8 years ago