Trivial Proofs - Discrete Mathematics and its Applications - Lecture Slides, Slides for Discrete Mathematics. Shoolini University of Biotechnology and Management Sciences

Discrete Mathematics

Description: During the study of discrete mathematics, I found this course very informative and applicable.The main points in these lecture slides are:Trivial Proofs, Methods of Proof, Rules of Inference, Proof Strategies, Vacuous Proofs, Empty Set, Postive Integers, Example Indirect Proof, Proof by Contradiction, Common Divisor, Equivalence Proofs, Theorems with Quantifiers
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Lecture 11
1.5, 3.1 Methods of Proof
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Last time in 1.5
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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