Question

How to find upper and lower bounds in hasse diagram

Answer 1

For the greatest lower bound just turn the Hasse diagram upside-down and then find the least upper bound in the inverted diagram. If you do that with e and t, for instance, in the partial order in my answer, you’ll find that their glb is r.Once you’ve done this a few times, you should be able to do it without actually turning the diagram upside-down: the glb of x and y is the highest element u such that u≤x and u≤y. That means that if z is any lower bound of x and y, then z≤u.