# Library Exercise_4_2_1_10

Require Import Utf8.

Set Implicit Arguments.

Generalizable All Variables.

## Problem

Let

S = {1, 2, 3, 4} : Ob Set. What is the automorphism group
of

S in

Set, and how many elements does this group have? What
is the endomorphism monoid of

S in

Set, and how many
elements does this monoid have?

Recall from Example 4.1.2.3 that every group has an underlying
monoid

U(G); is the endomorphism monoid of

S the underlying
monoid of the automorphism group of

S?