Recall that the monad List: \$$Set \rightarrow Set\$$ that sends a set X to the set of lists of elements of X, whose multiplication flattens a list of lists, and whose unit takes an element \$$x \in X\$$ to the singleton list [x] \$$\in\$$ List(X).

(a) Given a List-algebra \$$a: List(X) \rightarrow X\$$, construct a monoid on the set X.

(b) Given a monoid (X,*,e), construct a list algebra

(c) Show that your two constructions are inverses (we hope they are!)