   Chapter 2.1, Problem 11E

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 ) ( z + w ) = x z + x w + y z + y w

To determine

To prove: The statement, ‘(x+y)(z+w)=xz+xw+yz+yw’ for all x,y,z, and w in Z.

Explanation

Formula Used:

Subtraction:

Subtraction is defined by xy=x+(y) for arbitrary x and y in Z.

The distributive law:

x(y+z)=xy+xz holds for all elements x,y,zZ.

x+y=y+x for arbitrary x,yZ.

Proof:

Consider x,y,z,wZ.

(x+y)(z+w)=(x+y)z+(x+y)w

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

A population of N = 7 scores has a mean of = 13. What is the value of X for this population?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 914, evaluate the expression. 13. (323)(435)293

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

The arc length function for y = x2, 1 x 3 is s(x) = a) 1x1+4x2dx b) 1x1+4t2dt c) 1x1+t4dt d) 1x1+4t4dt

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 