relations and functions

[sbrajagopal2690]

need help on this ..any suggestions are highly appreciated


Consider the set of positive rational numbers Q+ . Consider the relation r defined by
(x,y) ∈ r<=> x/y ∈ Z. Show that r is a partial order and determine all numbers greater than 1/2.

 

[HallsofIvy]

I presume that you know that the only condition for an "order relation" is that it be "transitive": if (x, y) and (y, z) then (x, z). Here, that means you must show that if x/y is an integer and y/z is an integer then x/z is an integer.

As for "determine all numbers greater than 1/2", you have defined a relation, (x, y), but have NOT said which of x or y is to be considered "larger". My guess would be the "x" but that should be explicitely said.