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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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Label each of the following statements as either true or false.

If a set is closed with respect to the operation, then every element must have an inverse.

To determine

Whether the statement, “If a set is closed with respect to the operation then every element must have an inverse” is true or false.

Explanation

Explanation:

Consider the statement, “If a set is closed with respect to the operation then every element must have an inverse’.

Consider the set ={...,3,2,1,0,1,2,3,...} of integers.

Multiplication of two integers is always an integer. So, the set is closed with respect to multiplication.

As 2 is an integer, 2.

Also, 2×12=1

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