   Chapter 1.7, Problem 18E

Chapter
Section
Textbook Problem
1 views

# Let ℘ ( A ) be the power set of the nonempty set A , and let C denote a fixed subset of A .Define R on ℘ ( A ) by x R y if and only if x ∩ C = y ∩ C . Prove that R is an equivalence relation on ℘ ( A ) .

To determine

To prove: R is an equivalence relation on (A) where (A) is the power set of the nonempty set A, and C is a fixed subset of A and R is a relation defined on (A) by xRy if and only if xC=yC.

Explanation

Formula Used:

A relation R on a nonempty set A is equivalence if the following properties are satisfied:

(1) xRx for all xA. (Reflexive Property)

(2) If xRy, then yRx. (Symmetric Property)

(3) If xRy and yRz, then xRz. (Transitive Property)

Proof:

Let x,y,z(A).

1. xRx,sincexC=xC.

So, R is reflexive.

2

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 