354442_Tutorial_02-Set, Relations, function (updated Nov 2020).pdf

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TMA1211 Discrete Mathematics and ProbabilityTutorial 2Updated Nov 20201Tutorial 2: Sets, Relations & Functions1. LetX= {1, 2},Y= {2, 3} andZ= {3, 4, 5}. Find the Cartesian productXxYxZ.2.Determine whether the relationRon the set of integers is reflexive, symmetric, antisymmetric, and/or transitive,where (x,y)Rif and only ifx + y = 0.3.Given the relation R = {(1,2), (1,3), (2,4), (3,1), (4,2), (5,4)} on the set S = {1,2,3,4,5}.a) Draw the directed graph (or digraph) of R.b) Find R1.c) Find R*.4.Let S = {1, 2, 3, 4, 5}, and the relation R on S is defined by (a, b)R if and only if ab.a) List all the elements of R.b) Represent R with a matrix.c) Show that R is a partial ordering.
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Order theory, Binary relation, Transitive relation, Total order

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