Let f, g: Bn → B. Define the relation "<" on Fn, the set of all Boolean functions of n variables, by f ≤ g if the value of g is 1 at least whenever the value of f is 1.
(a) Prove that this relation is a partial order on Fn.
(b) Prove that fg ≤ f and f ≤ f + g.
(c) For n = 2, draw the Hasse diagram for the 16 functions in F2. Where are the minterms and maxterms located in the diagram? Compare this diagram with that for the power set of {a, b, c, d] partially ordered under the subset relation.