Partial problem set 10 - 1 2 3 4 5 6 A A A A A A Reflexive let a a a = 0 Since 0 is an integer aRa Symmetric let a,b and aRb This means that a b is an

Partial problem set 10 - 1 2 3 4 5 6 A A A A A A Reflexive...

This preview shows page 1 - 2 out of 2 pages.

1. A 2. A 3. A 4. A 5. A 6. A) Reflexive: let a ∈ ℝ. a - a = 0. Since 0 is an integer, aRa. Symmetric: let a,b ∈ ℝ and aRb. This means that a - b is an integer. since b - a is equal to -1 times (a - b), b - a must be an integer as well, so bRa and aRb. Transitive: let a,b,c ∈ ℝ. This means that a - b is an integer and b - c is an integer. The sum of those two expressions is a - c, which must also be an integer, so aRc. Since R is reflexive, symmetric, and transitive, R is an equivalence relation on ℝ. B) All integers are in [1]. C) All odd multiples of ½ are in [1/2]. 7. A) 3 equivalence relations on {1,2,3} 1. All 3 in the same equivalence class 2. 1, 2, and 3 by themselves in their own classes 3. Two of the elements together in one class and the other by itself B) 5 equivalence relations on {1,2,3,4} 1. All 4 elements in the same equivalence class 2. Each element in its own class 3. Three elements in the same class, one on its own 4. One pair in one class, one pair in another 5. One pair in one class, and the other two in their own separate classes.
Image of page 1
Image of page 2

You've reached the end of your free preview.

Want to read both pages?

  • Fall '08
  • Knight,J
  • Binary relation, Transitive relation, Symmetric relation, Total order, aRb, total order relation

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

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes
A+ icon
Ask Expert Tutors