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

## Notes Information

 Material Type: Class Note Professor: Staff Class: CMSC 250 - Discrete Structures Subject: Computer Science University: University of Maryland Term: 2007 Keywords: ContradictionImmediatelyDefinitionsContrapositiveRational NumberSubstitutionPropositionalInfinite SetsGeneralizationTransitivity      ## Sample Document Text

CMSC 250 Discrete Structures Number Theory 20 June 2007 Number Theory 2 Exactly one car in the plant has color square6 H(a) := "a has color" square6 ?x?Cars - H(x) ? square4 ?a?Cars - a ? x ? ~ H(a) square6 H(a,b) := "a has color b" square6 ?x?Cars - ?y?Colors square4 H(x,y) ? - ?a?Cars, ?b?Colors square4 a ? x ? ~ H(a,b) 20 June 2007 Number Theory 3 At most one car in the plant has color square6 H(a,b) := "a has color b" square6 ?x,a?Cars - ?y,b?Colors square4 [H(x,y) ? H(a,b)] ? x = a 20 June 2007 Number Theory 4 At least two cars in the plant have color square6 H(a,b) := "a has color b" square6 ?x,a?Cars - ?y,b?Colors square4 H(x,y) ? H(a,b) ? x ? a 20 June 2007 Number Theory 5 Existential Gen/Inst square6 Existential Generalization - P(value) - value ? D ??x?D such that P(x) square6 Existential Instantiation - ?x?D such that P(x) ?P(a), a?D such that P(a) is true 20 June 2007 Number Theory 6 Proofs Must Have! square6 Clear statement of what you are proving square6 C...

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