LN6(Equivalence Relation)

LN6(Equivalence Relation) - Equivalence Relation Reflexive...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Equivalence Relation Reflexive, Symmetric, and Transitive
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Definition . A binary relation on a set is called an equivalence relation if it is reflexive, symmetric, and transitive. Example . Let and
Image of page 2
The table below gives the properties of the five relations. Relation Reflexive Symmetric Transitive No Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Therefore, and are equivalence relations on while and are not.
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Definition . Let be an equivalence relation on a set . For each , we define the equivalence class of , denoted by the symbol , to be the following subset of : Example . Let and consider the equivalence relation . Then the equivalence classes are:
Image of page 4
Note that there are just two distinct equivalence classes because . The other equivalence class is .
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern