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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!)