Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Math Topics » discretemath

Topic: Equivalence relation
Replies: 3   Last Post: Jun 7, 2013 4:11 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Ming Wang

Posts: 3
From: USA
Registered: 3/25/13
Equivalence relation
Posted: Mar 25, 2013 3:31 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Describe the resulting figure.
Let A be the set of points in the rectangle with x and y
coordinates between 0 and 1. That is,
A = {(x, y) ? R × R| 0 ? x ?1 and 0? y ? 1}.
Define a relation R on A as follows: For all (x1, y1) and (x2, y2) in A,
(x1, y1) R (x2, y2) ?
(x1, y1) = (x2, y2); or
x1 =0 and x2 =1 and y1 = y2; or
x1 =1 and x2 =0 and y1 = y2; or
y1 =0 and y2 =1 and x1 = x2; or
y1 =1 and y2 =0 and x1 = x2.
In other words, all points along the top edge of the rectangle
are related to the points along the bottom edge directly
beneath them, and all points directly opposite each other
along the left and right edges are related to each other.
The points in the interior of the rectangle are not related to
anything other than themselves. Then R is an equivalence
relation on A. Imagine gluing together all the points that
are in the same equivalence class. Describe the resulting
figure.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.