e611k - MAD 2104 Quiz 6 key Prof S Hudson 1[30pts Find the...

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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 70-100 B’s 60-69 C’s 50-59 D’s 40-49 I’ve averaged your best 5 of 6 quiz grades in the corner. This does not yet include the HW or the final. The class average for this stat is approx 70 / 100. The scale for it is A’s 80-100
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