   Chapter 8.3, Problem 32ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Let A be the set of all straight lines in the Cartesian plane. Define a relation || on A as follows:For every l 1 and l 2 in A, l 1 | | l 2   ⇔ l 1   is   parallel to  l 2 . Then || is an equivalence relation on A. Describe the equivalence classes of this relation.

To determine

Describe the equivalence classes of the given relation.

Explanation

Given information:

Let A be the set of all straight lines in the Cartesian plane. Define a relation || on A as follows:

For all l1 and l2 in A, l1, l2 ⇔ l1 is parallel to l2.

Then is an equivalence relation on A.

Calculation:

A=Set of all straight lines in the Cartesian plane ={(p,q)A×A|p and q are parallel}

We know that is an equivalence relation.

Two straight lines are related if they are parallel.

In general, the equation of a straight line is y = mx + b with m the slope and b the y -intercept. Two straight lines are parallel when they have the same slope and thus if they have the same value of m

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