exam2sol - COT 3100 Fall 00 Exam#2 Functions Relations...

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COT 3100 Fall ‘00 Exam #2 10/26/00 Instructor: Arup Guha Name: _______________ TA: _________________ Date: ________________

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for a correct answer, 0 for no response, and –1 for an incorrect response.) a) All functions are surjective. False b) The relation R={(1,3), (2,4), (5,7), (6,8)} True is transitive. c) Let f be a bijection from the finite set A to the True finite set B. |A| =|B|. d) If R is a non-empty relation, then so is R ° R. False e) If a relation R is symmetric, it contains an False even number of elements. f) A partial ordering relation must be True anti-symmetric. g) The total number of edges in a complete False graph with 5 vertices is 15. h) All walks are paths. False i) There exists a graph G such that the sum of the False degrees of its vertices is 9. j) If f: A B and g: B C are both injections, True then g ° f is as well. k) If a relation R is symmetric it can not be False anti-symmetric. l) Let [x] and [y] be equivalence classes in an True equivalence relation. [x]=[y] or [x] [y] = . m) For 2 relations R and S that are subsets of AxA, False R ° S = S ° R n) Let A={1,2,3}. The number of possible True relations R that are subsets of AxA is 2 9 . o) Let A={1,2,3}. Let R be a relation over AxA False such that R={(1,2),(2,1),(3,2)}. R is a bijection. 2) (8 pts) Let R and S be relations that are subsets of AxA. (A={1,2,3,4}. If R={(1,2), (1,3), (2,4), (3,1), (3,2), (4,4)} and S={(1,4), (2,1), (2,3), (3,2), (4,1), (4,2)}, then what is R ° S? {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1), (3,3), (3,4), (4,1), (4,2)}
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exam2sol - COT 3100 Fall 00 Exam#2 Functions Relations...

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