(a) If x-y>1, show that there is at least one n$\displaystyle \in$Z (integers) such that y<n<x.

For this should I try showing that there are no n's in Z? Essentially a proof by contradiction.

(b) if y<x, show there is a rational number z such that y<z<x.

At first i was thinking the transitive property (i think thats the name of the one i''m thinking of) but I don't seem to confident in it and i'm only recalling about relations like (a,b) (c,d) (a,d) etc.