MATHEMATICAL REASONING

MATHEMATICAL REASONING

1. Symbol

   • ( ~ ) negation
   • ( v ) disjunction
   • ( --> ) implication
   • ( ^ ) conjunction
   • ( <--> ) equivalence

2. MATHEMATICAL PROOF

   • Direct Proof
     • Proposition :
       • If p then q
         • • Truth Table:
   • Indirect Proof
     • Contrapositive
       • Outline
         • • Example:
           • Truth Table:
       • If p then q = ~q then ~p
     • Contradiction
       • Truth Table:
         • • Outline::
       • establishes the truth of a given proposition by the supposition that it is false and the subsequent drawing of a conclusion that is contradictory to something that is proven to be true
       • Broader usage
   • Mathematical Induction
     • Outline:
       • • (1) Basis step
         • (2) Inductive step
         • Table:
         • Use when proposition is in number sequence form

3. Even integer:

4. Odd integer:

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