   Chapter 2.1, Problem 5E

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)=xy, for all x,yZ, set of integers is Z.

Explanation

Formula Used:

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

The commutative law of multiplication is defined as xy=yx.

Proof:

Let us take L.H.S. of the given equality,

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

Rearrange the terms in R.H.S

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