Final,Midterms,Quizes,Homeworks,Worksheets

# Final,Midterms,Quizes,Homeworks,Worksheets - Math 55-2...

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Math 55-2 Final Exam Rob Bayer August 14, 2009 You have until 4:00pm to complete this test. No calculators, books, notes, or consultation with other members of the class are permitted. Your exam should have 9 pages. Unsupported or improperly supported answers will receive no credit. Name: 1 10 2 15 3 15 4 15 5 10 6 10 7 15 8 10 Total 100 1

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1. (10 pts) Short Answer. You need not show any work for this problem (a) A function f is injective iF (b) A relation R is an equivalence relation iF (c) Two events are called independent iF (d) Circle the countable sets: R Q Z × N P ( N ) (e) The linear congruence ax b (mod n ) has a solution iF (f) A function f : G 1 G 2 is an isomorphism of graphs iF (g) State Chebyshev’s Inequality (h) ±ind a Minimal Spanning Tree in the following graph. You may simply ²ll in the necessary edges 2 5 2 31 2 3 2 3 3 1 1 3 33 64 (i) ±ind a generating function for the number of solutions in non-negative integers to 2 x 1 +3 x 2 +4 x 3 = n 2
2. (15 pts) (a) Find a truth table for the compound proposition ( p q ) ( q ∧¬

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## Final,Midterms,Quizes,Homeworks,Worksheets - Math 55-2...

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