I've been struggling with this one.
Let A be a partially ordered set. Suppose X⊆Y⊆A.
1. Assuming that all the least upper bounds and greatest lower bounds exist, prove that glb(Y) ≤ glb(X) ≤ lub(X) ≤ lub (Y)
2. Find two subsets X and Y of Real Numbers for which X is a proper subset of Y and yet glb(Y) = glb(X) and lub(X) = lub(y)