MATHEMATICAL PROOF

MATHEMATICAL PROOF

1. Direct Proof

   • A mathematical argument uses rules of inference to derive the conclusion from the premise
     • Suppose p is true Therefore p→q Thus, q is true.
     • Proof by cases
       • sometimes it is not possible to construct a single "path" from hypothesis to conclusion,

2. Contrapositive Proof

   • proceeding this proving method like direct proof but using ¬q as hypothesis and ¬p as conclusion
     • Proof. Suppose Q is not true, ¬Q Therefore….. Thus P is not true, ¬P

3. Mathematical Induction

   • a mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number.
     • The technique involves two steps to prove a statement
       • Base step
         • It proves that a statement is true for the initial value.
       • Inductive step
         • It proves that if the statement is true for the nth iteration (or number n), then it is also true for (n+1)th iteration ( or number n+1).
     • • Base step
       • Inductive step

4. Proof by Contradiction

   • To prove a statement P is true, we begin by assuming P false and show that this leads to a contradiction; something that always false.
     • Suppose ¬p Therefore…. Thus C⋀¬C

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