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CMSC 150 Fall 2015 Section 7981 - Assignment 2, due November 1Problem 1:LetX= {1, 2, 3, 4} andY= {3, 4, 5, 6}.Define a relationQfromXtoYby therule:xQyif and only ifx>=y.a.Which of the following statements are true of the relationQ? .StatementTrue or False?Reason2 Q 44 Q 3(4,4) is in Q(7,3) is in Qb. WriteQas a set of ordered pairs. Be sure to use correct notation for both sets andordered pairs.Important hint: Check your answers to (a) and (b) for consistency with one another!In Problems 2 and 3, you are given a binary relation on a set.Determine whether the relation is(a) reflexive, (b) symmetric, (c) transitive.If your answer to any of the questions about therelation is No, give a specificcounterexample. (There is no need to give more than onecounterexample to justify a "No".)Problem 2:Set: {0, 1, 2, 3}Relation: {(0,0), (0,1), (1,1), (1,2), (2,2), (2,3), (3,3)}Reflexive?Symmetric?Transitive?Problem 3:Set: the setZof integers.Relation O:mOnmeansm–nis odd.Reflexive?Symmetric?Transitive?Hint: Experiment with a couple dozen examples first.Problem 4:Draw a directed graph to represent the relationRonA, whereA= {1, 2, 3, 4, 5} andR = {(1,2), (1,3), (2,2), (2,4), (4,5)}.Problem 5:LetA= {a,b,c,d,e,f} be partitioned into subsets {a,b}, {c,e,f}, and {d}.Illustrate the corresponding equivalence relation by a directed graph.1

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