   Chapter 2.1, Problem 1E

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 = 0

To determine

To prove: The equality x0=0, for all xZ, set of integers is Z.

Explanation

Formula Used:

The formula used is definition of subtraction expressed as xy=x+(y).

Proof:

Since 0=0+0

Multiply x on both sides.

x0=x(0+0)

Thus, by distributive law,

x(0+0)=x0+x0x0+x0=x0

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