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Unformatted text preview: MAD 2104 Nov 10, 2011 Quiz 6 key Prof. S. Hudson 1) [30pts] Find the number of edges in each of these special graphs. Show work (hopefully not just a drawing) and label your answers clearly. a) G = Q 5 b) G = K 7 c) G = W 9 2) [40pts] Define R = { ( a,b ) ∈ N × N : a  b } , a relation on the set of natural numbers. Define ( a,b ) ∈ S to mean a < b . a) Describe the relation R ◦ S as simply as possible. [If you cannot describe it, list two ordered pairs that belong to it, and two that do not, with reasoning]. b) Circle the properties that R has (and only those), among these four. You do not have to justify your answers. reflexive , symmetric , antisymmetric , transitive 3) [30pt] Prove Thm 1 from 8.1; R is transitive on A if and only if R n ⊆ R for n = 1 , 2 , 3 ... You can answer on the back. Remarks and Answers; The average was about 60 / 100. The scale is; A’s 70100 B’s 6069 C’s 5059 D’s 4049 I’ve averaged your best 5 of 6 quiz grades in the corner. This does not yet include theI’ve averaged your best 5 of 6 quiz grades in the corner....
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This note was uploaded on 12/27/2011 for the course MAD 2104 taught by Professor Staff during the Fall '08 term at FIU.
 Fall '08
 STAFF

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