   Chapter A.3, Problem 6E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Does the Transitive Property of Inequality hold true for four real numbers a, b, c, and d? That is, is the following statement true?If a < b , b < c , a n d     c < d ,     t h e n     a < d .

To determine

To find:

To show that the following statement is true, a<b,b<c,and c<d, then a<d.

Explanation

Consider the following statement,

3<7

Definition:

If a is less than b a<b if and only if there is a positive number p for which

a+p=b;

a is greater than b a>b if and only if b<a.

Transitive Property of Inequality:

For number a, b, and c, if a<b and b<c, then a<c.

First a<b then by using the definition to get a+p1=b..........(1)

Then, b<c then by using the definition to get b+p2=c.........(2)

Then c<d then by using the definition to get c+p3=d.......(3)

Substitute (2) in (3) to get the following,

c+p3=db+(p2+p3)=d

Substitute (1) in the above equaiton to get the following,

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