   Chapter 1.4, Problem 8TFE

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Textbook Problem
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# True or FalseLabel each of the following statements as either true or false.An identity and inverses exist in a set containing a single element upon which a binary operation is defined.

To determine

Whether the statement, “An identity and inverses exist in a set containing a single element upon which a binary operation is defined” is true or false.

Explanation

Formula Used:

Let * be a binary operation on the nonempty set A. An element e in A is said to be the identity element with respect to the binary operation if e has the property that

xe=ex=x for all xA.

Let e be the identity element for the binary operation * on the set A, and let aA. If there exists an element bA such that a*b=e and b*a=e holds

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