MD 1. \$$\Delta\$$ is monotonic, because \$$a \leq b \to (a,a) \leq (b,b)\$$, by definition of \$$\leq_{A\times A}\$$

MD 2. By the method in lecture 6, r(y,z) = least upper bound of X = \$$\\{x : \Delta (x) \leq (y,z) \\}\$$. Since X is the set of elements of A less than min(y,z), r(y,z) is min(y,z).

MD 3. By duality, l(y,z) = max(y,z)

MD 4.

r: least upper bound of X = \$$\\{x : \Delta (x) \leq (y,z) \\}\$$: least common multiple

l: greatest lower bound of X = \$$\\{x : \Delta (x) \geq (y,z) \\}\$$ : greatest common divisor

I think I've been sloppy and got some of this flipped - to be fixed later.