   Chapter 8.3, Problem 1ES ### 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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# Suppose that S = { a , b , c , d , e } and R is a relation on S such that a R b,b Rc, and dRe. List all of the following that must be true if R is (a) reflexive (but not symmetric or (transitive). (c) synnetric (but not reflexive or symmetric), and (d) an equivalence relation. c   R   b                     c   R   c             b R   a c   R   d                     e   R   a             b R   a

To determine

(a)

To list all of the following that must be true if R is reflexive (but not symmetric or transitive).

c R b c R c a R c b R a a R d e R a e R d c R a

Explanation

Given information:

Suppose that S = { a, b, c, d, e } and R is a relation on S such that a R b, b R c, and d R e.

Calculation:

S={a,b,c,d,e}a R bb R cd R e

We need to determine which of the following cRb, cRc, aR

To determine

(b)

To list all of the following that must be true if R is symmetric (but not reflexive or transitive):

c R b c R c a R c b R a a R d e R a e R d c R a

To determine

(c)

To list all of the following that must be true if R is transitive (but not reflexive or symmetric):

c R b c R c a R c b R a a R d e R a e R d c R a.

To determine

(d)

To list all of the following that must be true if R is: an equivalence relation.

c R b c R c a R c b R a a R d e R a e R d c R a.

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