Lecture 11

1.5, 3.1 Methods of Proof

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To prove theorems we use rules of inference such as:

p, pq, therefore, q

NOT q, pq, therefore NOT p.

p AND q, therefore p

FORALL x P(x), therefore for arbitrary c, P(c)

EXISTS x P(x), therefore for some c, P(c)

It is easy to make mistakes, make sure that:

1) All premises pi are true when you prove (p1 AND p2 AND...pn) q

2) Every rule of inference you use is correct.

Some proof strategies:

To proof pq

1) direct proof: assume p is true, use rules to prove that q is true.

2) indirect proof, assume q is NOT true, use rules to prove p is NOT true.

To prove p is true:

3) By contradiction: assume p is NOT true, use rules to show that NOT pF

i.e. it leads to a contradiction.

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Shoolini University of Biotechnology and Management Sciences

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Discrete Mathematics

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27/04/2013