HW3 Problem 3

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Problem 3

Read the explanation about a proof synopsis on pg. 35, then write a proof synopsis of Theorem 3.13.

Solution

Suppose both $e, \bar{e}$ are the identity elements of $S$, then use the definition of identity element for $*$$(e*s=s*e=s)$ to show $e= \bar{e}$ which means an identity element must be unique.