   Chapter 2.1, Problem 6E

Chapter
Section
Textbook Problem

Prove that the equalities in Exercises 1 − 11 hold for all x , y , z   and   w in Z . Assume only the basic postulates for Z and those properties proved in this section. Subtraction is defined by x − y = x + ( − y ) . x − 0 = x

To determine

To prove: The equality x0=x, for all xZ, set of integers is Z.

Explanation

Formula Used:

The formula used is the property of subtraction is defined by xy=x+(y).

The property of additive identity is defined as a+0=0 then 0 is additive identity.

Proof:

Consider 0 is the additive identity and 0Z.

x+0=x by the property of additive identity

Again

x(0)

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