# Relations Problem 1

First, notice that your base set is $$\mathbb{Z}^2$$. That is, each object in the base set is a 2D point with integer coordinates. The relation $$\ll$$ relates a 2D point to another 2D point.

Now, recall what it means for a relation R on a set A to be transitive:

For any elements s,t,w in A, if sRt and tRw, then sRw.

For this problem, the elements s, t, w are all 2D points. So your proof will be manipulating three 2D points. E.g. p in the above definition would become something like (a,b) in your proof.

Now write out the hypothesis sRt and tRw using 2D points and the relation name $$\ll$$. Same with the conclusion sRw.

Finally, you'll need to apply the definition of $$\ll$$ to the information in both the hypothesis and the conclusion. You should now be left with an algebra problem to solve.