   Chapter 8.5, Problem 4ES ### 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 R be the “less than” relation on R, the set of all real number: For every x , y ∈ R , x R y ⇔ x < y . Is R antisymmetric? Prove or give a counterexample.

To determine

To check:

Whether R is antisymmetric or not.

Explanation

Given information:

Let R be the “less than” relation on the set of all real numbers:

For all a,yR,xRyx<y.

Concept used:

A relation R on a set A is said to be antisymmetric if and only if for all a and b in A, if aRb and bRa then a=b.

Calculation:

The objective is to determine whether R is antisymmetric or not.

Let R be the relation defined on the set as.

R={(x,y)×|x<y}

Let (x,y)R and (y,x)R

By the definition R

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