   Chapter 12.3, Problem 15ES ### 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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# Prove property (12.3.5).

To determine

To prove:

Each k -equivalence class is a subset of a (k1) - equivalence class for every integer k1.

Explanation

Given information:

The given statement is, “Each k -equivalence class is a subset of a (k1) - equivalence class for every integer k1 ”.

Proof:

Let k be a positive integer. Let A be an automaton and let Ck be a k -equivalence class of A.

Let s and t be two states in Ck.

Since s and t are two states in the same k -equivalence class, s and t are k -equivalent.

We know that if two states are k -equivalent, then they are also (k1) - equivalent. Thus, s and t are (k1) - equivalent.

This then implies that there exist a (k1) - equivalence class Ck1 that contains both s and t

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