# Equivalence Relations and Classes

Not what you're looking for?

Let L be a subset of {a,b}*

Define a relation R (R sub L) on S* as follows:

L

for All of x, y is a member of S*,

(x,y) are members of R if for all of z, xz are members of L iff yz are members of L

A) Show that R is an equivalence relation

B) Suppose L={a^i b^i where i >= 0}

What can you say about the index of R (number of classes)? is it finite or infinite?

Show some classes and elements in these classes to justify your answer?

c) Suppose L={a^i b^j where i,j >= 0}

What can you say about the index of R (number of classes)? is it finite or infinite?

Show some classes and elements in these classes to justify your answer?

D) Suppose L={a^i b^3i where i >= 0}

What can you say about the index of R (number of classes)? is it finite or infinite?

Show some classes and elements in these classes to justify your answer?

Note: ^ means to the power, so a^i means a to the power of i.

##### Purchase this Solution

##### Solution Summary

Equivalence relations and classes are investigated. The solution is well presented.

##### Solution Preview

Please see the attachment.

First, let's clarify the definitions.

is a set of sequences of 's and 's. If we can define multiplications for and , then . is a subset of . The relation defined ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Probability Quiz

Some questions on probability

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.