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
Showing pages  1  -  2  of  15
Lecture 11
1.5, 3.1 Methods of Proof
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 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.
The preview of this document ends here! Please or to read the full document or to download it.
Document information
Embed this document:
Docsity is not optimized for the browser you're using. In order to have a better experience please switch to Google Chrome, Firefox, Internet Explorer 9+ or Safari! Download Google Chrome