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Lecture Notes for CMSC 250 - Discrete Structures with Plane at Maryland (UMD)

Notes Information

Material Type:Class Note
Professor:Plane
Class:CMSC 250 - Discrete Structures
Subject:Computer Science
University:University of Maryland
Term:Fall 2004
Keywords:
  • Contrapositive
  • Definitions
  • Contradiction
  • Interpretation
  • Infinite Sets
  • Propositional
  • Unique Factorization
  • Contraposition
  • Positive Integers
  • Counter Example
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Sample Document Text

1 Proof Must Have . Statement of what is to be proven. . "Proof:" to indicate where the proof starts . Clear indication of flow . Clear indication of reason for each step . Careful notation, completeness and order . Clear indication of the conclusion Number Theory - Ch 3 Definitions . Z --- integers . Q - rational numbers (quotients of integers) - r?Q $a,b?Z, (r = a/b) ^ (b " 0) . Irrational = not rational . R --- real numbers . superscript of + --- positive portion only . superscript of - --- negative portion only . other superscripts: Zeven, Zodd , Q>5 . "closure" of these sets for an operation 2 Integer Definitions . even integer - n ?Zeven $k ? Z n = 2k . odd integer - n ? Zodd $k ? Z n = 2k+1 . prime integer (Z>1) - n ?Zprime "r,s?Z+, (n=r*s) fi(r=1)v(s=1) . composite integer (Z>1) - n ? Zcomposite $r,s?Z+, n=r*s ^(r"1)^(s"1) Constructive Proof of Existence If we want to prove: . $n?Zeven, $p,q, r,s?Zprime n = p+q ^ n = r+s ^p"r^ p"s^ q"r^ q"s ...

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