   Chapter 8.2, Problem 26ES ### 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. Let A be the set of all strings of 0’s, 1’s, and 2’s that have length 4 and for which the sum of the charaters in the string is less than or equal to 2. Define a relation R on A as follows: For every s , t ∈ A , s R t ⇔ the sum of the characters of s equals the sum of the characters of t.

To determine

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

Explanation

Given information:

Let A be the set of all strings of 0’s, 1’s and 2’s of length 4. Define a relation R on A as follows: For all s, t ∈ A, s R t ⇔ the sum of the characters in s equals the sum of the characters in t.

Calculation:

Reflexive:

Since the relation is based on the sum of characters in a string, s = s, so sAs.

Thus, reflexive

Symmetric:

Suppose s and t are strings. If sAt, then s and t have the same sum of their characters, so tAs

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