Question

Let S = {0,1,2,3,4,5,6,7,8}. Test the following binary relation on S for reflexivity, symmetry, antisymmetry, and...

    1. Let S = {0,1,2,3,4,5,6,7,8}. Test the following binary relation on S for reflexivity, symmetry, antisymmetry, and transitivity. xρy if and only if x+y = 8.
  2. Is ρ an equivalence relation?
  3. If we change the relation to x ρ y if and only if x+y 6 8 how will the cardinality of ρ change? Give a detailed explanation.

2. draw the Hasse diagram for the partial ordering “x divides y” on the set {24,3,4,12,96,15,21,36}. Name any least elements, minimal elements, greatest elements, and maximal elements. Explain in full detail how did you obtain every single one of them.

Math   Statistics-And-Probability   
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