   Chapter 2.1, Problem 9E

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 + y ) = ( − x ) + ( − y )

To determine

To prove: The equality (x+y)=(x)+(y), for all x,yZ, set of integers is Z.

Explanation

Formula Used:

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

The commutative law for addition is defined as x+y=y+x.

The distributive law is defined as x(y+z)=xy+xz.

Proof:

Consider x,y,zZ,

(x+y)=(1)(x+y)=(1)(x)

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