1_MATHEMATICAL PROOF STRATEGIES

1_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. 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

3. INDIRECT METHOD

   • 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
   • CONTRAPOSITIVE PROOF
     • • p --> q is logically equivalent to ~ q --> ~ p
     • Alternative to direct proof
     • Assume ~Q is true to deduce that ~P is true

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