Methods of proof

  • A proof is a statement which arises as a result of true statements. The last statement is called the conclusion and each statement before it are called the premise or hypotheses or assumption.

  • The rules of inference are
    1. Law of detachment (or Modus Ponens):
      pqp→qp→q∧p
      TTTT
      TFFF
      FTTF
      FFTF

    2. Law of contraposition or Modus Tollens: p→q∧∼q

  • Different methods of proof:
    1. Direct proof: A proof of p⇒q begins with the assumption that p is true and with the repeated use of laws of detachment proves that q is true.

    2. Indirect proof: ∼p⇒∼q i.e.(p⇒q)≡(∼p→∼q)

    3. Counterexamples: A counterexample to a statement p proves that p is false i.e. ∼p is true.



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