dm-lec6-mathInduction-s

# dm-lec6-mathInduction-s - Discrete Mathematics CS204...

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Discrete Mathematics CS204 Lecture #5 September 14, 2009 at KAIST 1

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Review Recall that - Proof by examples does not count as a proof unless the examples are exhaustive. - Among methods of direct proofs, there are Constructing a counterexample for negation of a universally quantified statement, Constructing an example for an existentially quantified statement, Proving both directions of implication for a propositional equivalence, 2
- Among methods of indirect proofs, there are Proof by contradiction, Proof by contrapositive, Nonconstructive existence proof. 3

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Induction and Deduction - In inductive reasoning, we collect evidences that support a general rule. Many important scientific discoveries are due to inductive reasoning. Essentially, it is the mathematically wrong method of proof by examples 4
- In deductive reasoning, we show that the truth of the conclusion is a logical consequence of given premises.

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