MATHEMATICAL PROOF STRATEGIES

MATHEMATICAL PROOF STRATEGIES

1. DIRECT PROOF

   • The most straight forward approach use to prove conditional statements are true.
   • Assume P is true and then shows the forces Q to be true

2. CONTRADICTION

   • To prove any kind of statement, not limited to proving just conditional statement
   • Assume that P is false, so ~P is true and deduces C^~C
   • ~p --> ( c --> ~c)
   • Used when direct and contrapositive approaches are not seem to work

3. CONTRAPOSITIVE PROOF

   • Alternative to direct proof
   • p --> q is logically equivalent to ~ q --> ~ p
   • Assume ~Q is true to deduce that ~P is true
   • • NURUL SHAFIKAH BINTI IDRIS
     • SITI NURSYAZANA HANISAH BINTI AZIDI
     • SET 2

4. MATHEMATICAL INDUCTION

   • It is used when we have a set of statements S1,S2,S3,...,Sn,..., and we need to prove that they are all true.
   • Conjecture
     • The sum of the first n odd natural numbers equals n2
   • if the base case is true, then all the cases in that particular problem are true

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