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## Homework Statement

Suppose r and s are two positive real numbers. Let D

_{r}and D

_{s}be defined as in part 3 of Example 4.3.1. What is [tex]D_r \circ D_s[/tex]? Justify your answer with a proof. (Hint: In your proof, you may find it helpful to use the triangle inequality.)

## Homework Equations

Example 4.3.1:

For each positive real number r, let D

_{r}= [tex]\left\{(x,y)\in \mathbb{R} \times \mathbb{R} | ( |x - y| < r \right\}[/tex]. Then D

_{r}is a relation on [tex]\mathbb{R}[/tex].

[tex]\circ[/tex] = composition

## The Attempt at a Solution

I don't know what the composition of D

_{r}and D

_{s}would be, so I am not even close to being able to prove anything.

thanks

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