Draw a Hasse diagram for each of the following partial orders. Find the maximal and minimal elements and determine whether the partial order is a total order.

a. is a partial order on the set {, , , , , } such that (, ) if and only if .

b. is a partial order on the set {, , , , , } such that (, ) if and only if is divisible by . Hint: An integer is divisible by an integer with 0 if and only if there exists an integer such that = .