   Chapter 8.5, Problem 47ES ### 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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# Use the algorithm given in the text to find a topological sorting for the relation of exercise 20.

To determine

To find:

A topological sorting for the “ R ” relation on the set s={0,1},

where R is defined by (a,b,c)R(d,e,f)ad,beandcf.

Explanation

Given information:

S={0,1}

Concept used:

(a,b,c)and(d,e,f)inS×S×S,

Calculation:

The beginning of the total order is:

Total order: (0,0,0)

Set A1=A{(0,0,0)}. You can indicate this by removing (0,0,0) from the Hasse diagram as

Shown below.

Next, choose the minimal element from A1{(0,0,0)}. You have three choices

(0,1,0),(1,0,0)and(0,0,1) .Say you pick (0,0,1). The total order thus far is

Total order: (0,0,0)&(0,0,1)

Set A1=A{(0,0,0)}{(0,0,1)}=A{(0,0,0)(0,0,1)}

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