Is on Z an equivalence relation How would one provehow this is so.pdf

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Is | on Z an equivalence relation? How would one provehow this is so. It does not clearly state in the given answer onthe first page. Solution 1) reflexive - for all x, xRx. 2) transitive - if xRy and yRz then xRz. 3) symmetric - if xRy then yRx. Now we can test this for all x in Z. 1) is it true that for all x in Z, that x | x? No. What about0? 2) if x | y and y | z does this mean that x | z? Well, let\'sthink about this. If x | y then y = k*x, where k is aninteger. The same goes for y | z, and z = p*y where p is aninteger. So we can substitute in for y, k*x and we get z =p*k*x, and since p*k is an integer we know that x | z. Sothis one is true. 3) if x | y does y | x? I think we can see from what we workedout in 2) that this is not necessarily true. So, we found out that | does not satisfy the requirements foran equivalence relation on Z..

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