   Chapter 8.2, Problem 9ES ### 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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# In 9-33, determine whether the given relation is reflexive symmetric, transitive, or none of these. Justify your answer.R is the “greater thean or equal to” relation on the set of real numbes: For every x , y ∈ R,   x   R y   ⇔ x ≥ y .

To determine

To determine whether the given relation is reflexive, symmetric, transitive, or none of these.

Explanation

Given information:

R is the “greater than or equal to” relation on the set of real numbers:

For all x, y ∈ R, x R y ⇔ x = y

Calculation:

Let us consider the given relation R as

R={x,yR|xy}

Reflexive:

The relation R is reflective if (a,a)R for every element aA.

We note that R contains (x,x) as xx for all xR and thus R is reflexive.

Symmetric:

The relation R on a set A is symmetric if (b,a)R whenever (a,b)R for a,bA.

We note that (0,1)R as 10, but (0,1)R as1 < and thus R is not symmetric

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