## Notes Information

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## 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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