Let A = {1, 2, 4, 6, 8} and, for a, b ∈ A, define a, b if and only if is an integer.(a) P...

Let A = {1, 2, 4, 6, 8} and, for a, b ∈ A, define a, b if and only if is an integer.

(a) Prove that < defines a partial order on A.

(b) Draw the Hasse diagram for ≤.

(c) List all minimum, minimal, maximum, and maximal elements.

(d) Is (A, ≤) totally ordered? Explain.