   Chapter 1.4, Problem 10E

Chapter
Section
Textbook Problem

Prove or disprove that the set Z − { 0 } of all nonzero integers is closed with respect toa. addition defined on Z .b. multiplication defined on Z .

(a)

To determine

Whether the set Z{0} of all nonzero integers is closed with respect to addition defined on Z.

Explanation

Consider the set of all nonzero integer Z{0}.

The addition operation on Z is defined as

xy=x+y, where x,yZ.

Substitute 1 for x and 1 for y in xy=x+y

(b)

To determine

Whether the set Z{0} of all nonzero integers is closed with respect to multiplication defined on Z.

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