Let (S, ) be a poset. We say that an element y S covers an element x S if x y and there is no element z S such that . The set of pairs (x,y) such that y covers x is called the covering relation of (S, )
What is the covering relation of the partial ordering {(a,b) a divides b} on {1,2,3,4,6,12}?
My answer so far is {(1,2), (1,3), (2,4), (2,6), (3,6), (4,12), (6,12)}
is this right?