MATH163 Midterm 2018-19 Fall Answer Keys.pdf - EASTERN...

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EASTERN MEDITERRANEAN UNIVERSITYDEPARTMENT OF MATHEMATICSMATH163 DISCRETE MATHEMATICS2018-2019 FALL SEMESTERMIDTERM EXAMANSWER KEYSQuestion 1:Use Venn diagrams to prove thatš“ āˆŖ(šµ\š“) =š“ āˆŖ šµ.)
Question 2:Consider relationš‘…= {(š‘„,š‘¦)|š‘„š‘‘š‘–š‘£š‘–š‘‘š‘’š‘ š‘¦,š‘„ āˆˆ š“,š‘¦ āˆˆ š“}on the setš“{2,3,4,5,10,12,25,30}.(a)Check whetherš‘…is reflexive, symmetric, antisymmetric and transitive. Justify youranswer in each case.(b)Ifš‘…is partial order, then draw Hasse diagram, find minimal and maximal elements anddecide on minimum and maximum.(c)Ifš‘…is equivalence relation, then determine the partition.=AnswerFREE SAMPLE
-š‘…is not symmetric, since, e.g.,(2,4)āˆˆ š‘…but(4.2)āˆ‰ š‘….

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Term
Spring
Professor
NoProfessor
Tags
Order theory, Transitive relation, Partially ordered set

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