   Chapter 8.3, Problem 14ES ### 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 each of 7—14, the relation R is an equivalence relation on the set A. Find the distinct equivalence classes of R. 14. A is the set of all strings of 0’s, l’s, and 2’s that have length 4 and for which the sum of the characters in the string is less than or equal to 2. R is defined 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 find:

The distinct equivalence classes of given relation R.

Explanation

Given information:

A is the set of all strings of 0’s, 1’s, and 2’s that have length 4 and for which the sum of the characters in the string is less than or equal to 2.

Calculation:

First, find the equivalence classes of every element of A, which has a sum of the characters of s equal the sum of characters of t.

={SA|SR00}={00}

Here, 00 has the equal length of 0.

={SA|SR01}={10}

Here, 01 and 10 have the equal length of 1.

={SA|SR11}={02,20}

Here, the strings are 11, 02and20 having the same length 2

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