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e610k

# e610k - I wrote your letter grade on your quiz in blue Also...

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MAD 2104 June 10, 2010 Quiz 6 Key Prof. S. Hudson 1) [10pts each] Given the matrix for a relation R below, find these 3 matrices (and label your 3 answers clearly!): a) the matrix for R - 1 b) the matrix for R c) the matrix for R 2 M R = 0 1 1 1 0 0 0 1 0 2) [40pts] Answer True or False: A circuit must begin and end at the same vertex. If the graph G contains a vertex a and H does not, then G is not isomorphic to H . If a simple graph G contains exactly 5 vertices, then its incidence matrix is 5 x 5. The 3-cube Q 3 is bipartite. There is a simple path between every pair of distinct vertices of a connected undirected graph. 3) [30pts] Choose ONE: (you can answer on the back): a) Prove that if R is transitive on a set A , then R n R for all positive integers n . b) Define a relation R on Z by R = { ( x, y ) : ( x + 1) 2 = ( y + 1) 2 } . Show that R is an equivalence relation. Remarks and Answers: The average among the top 20 students was 80 / 100. Here is a rough scale for the quiz, based mainly on that average: As 85 to 100 Bs 75 to 84 Cs 65 to 74 Ds 55 to 64 I wrote your letter grade on your quiz in blue. Also, the sum of your best 5 out of 6 quiz

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