How To Prove Conditional Statement??

How To Prove Conditional Statement??

1. INDIRECT METHOD

   • CONTRADICTION
     • If P, then Q
       • Method of Contradiction: Assume P and Not Q and prove some sort of contradiction.
     • example
     • suppose the statement to be proved is false
       • shows that this supposition leads logically to a contradiction
         • conclude that the statement to be proved is true
   • CONTRAPOSITIVE
     • If P, then Q
       • Method of Contrapositive: Assume Not Q and prove Not P.
     • example
     • Alternative to direct proof

2. DIRECT METHOD

   • DIRECT PROOF
     • Prove 'if p then q'
       • 1. Assume statement p is true
         • 2. Deduce statement q is true
           • This shows p-> q is true
     • example

3. MATHEMATICAL INDUCTION

   • MATHEMATICAL INDUCTION
     • STEPS
       • 1. Show it is true for the first one
         • 2. Show that if any one is true then the next one is true
           • Then, all are true
     • example

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