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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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Section
BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
20 views

Prove or disprove that the set B = { z 3 | z Z } is closed with respect to

a. addition defined on Z .

b. multiplication defined on Z .

a)

To determine

Whether the set B={z3|zZ} is closed under addition defined on Z or not.

Explanation

Given Information:

The set B={z3|zZ} under the operation addition defined on Z.

Explanation:

Consider the given set B={z3|zZ}.

Since, 1Z13=1B

b)

To determine

Whether the set B={z3|zZ} is closed under multiplication defined on Z or not.

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