Discrete Math

Which of these relations on {0, 1, 2, 3} are equivalence relations? Justify the relation(s) that are not equivalent.

R1: {(0,0), (1,1), (2,2), (3,3)}
R2: {(0,0), (1,1), (1,3), (2,2), (2,3), (3,1), (3,2), (3,3)}
R3: {(0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,2), (3,3)}

R1: This relations is equivalent
R2: This relation is equivalent
R3: This relation is not equivalent because:
• It is reflexive because the relation does contains (0,0), (1,1), (2,2), and (3,3).
• It is not symmetric because the relation contains (1,2), but not (2,1).
•This relation is transitive.

I think something is not right. . .Any suggestions? Thanks for any helpful replies!

  1. 👍
  2. 👎
  3. 👁
  1. I think I may have found the problem in my thinking:

    R2 is not equivalent right? Because it is not transitive.

    Justification:
    It is reflexive because the relation does contain (0,0), (1,1), (2,2), and (3,3).
    It is symmetric because the relation contains (1,3) ⋏ (3,1), and (2,3) ⋏ (3,2)
    Though the relation contains (1,3) ⋏ (3,2) it does not have (1,2), which means it is not transitive.

    1. 👍
    2. 👎
  2. R1: This relations is equivalent (agree)

    R2 is not equivalent right? Because it is not transitive. (agree)

    R3: This relation is not equivalent because the relation contains (1,2), but not (2,1) (agree)

    Excellent!

    1. 👍
    2. 👎
  3. Thank you for the reassurance.

    1. 👍
    2. 👎
  4. Keep up the good work!

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Mathematics

    Which of the following relations are functions ? F= {(1,2) (2,3) (3,5) (4,7)} G= {(1,3) (1,4) (2,5) (2,6) (3,7)} H= {(1,3) (2,6) (3,9), ..., (n, 3n), ... } Thanks you!

  2. world history

    How has the Armenian Genocide affected the foreign relations of Turkey and Armenia toward each other in recent decades? a.Turkey and Armenia have never established formal diplomatic relations. b.Turkey and Armenia have been

  3. algebra

    Can someone help with inverse relations and functions? is relation t a function? Is the inverse t a function? chart looks like: x 0 2 4 6 y -10 -1 4 8 If someone could please explain this problem

  4. algebra

    when ur given ordered pairs, how do you determine if the relations is a function

  1. database

    Given the Relational Model Notation below (in pages 156-157 of your book), extend it to define UNIQUE and NON-UNIQUE indexes for relations. The uppercase letters Q, R, S denote relation names. ■ The lowercase letters q, r, s

  2. database

    Given the Relational Model Notation below, extend it to define UNIQUE and NON-UNIQUE indexes for relations. The uppercase letters Q, R, S denote relation names. ■ The lowercase letters q, r, s denote relation states. ■ The

  3. math

    Which of the following relations is not a function? (8, 4), (-5, 2), (4, 1), (-6, 2) (-5, 4), (4, 2), (8, 1), (-6, 5) (-6, 4), (4, 3), (-5, 1), (8, 2) (4, 4), (-5, 2), (4, 1), (-6, 2) my answer is b

  4. Discrete Math

    Consider the following relations on R, the set of real numbers a. R1: x, y ∈ R if and only if x = y. b. R2: x, y ∈ R if and only if x ≥ y. c. R3 : x, y ∈ R if and only if xy < 0. Determine whether or not each relation is

  1. Math

    Which of the following relations has this characteristic: The relation is a function containing two ordered pairs. Reversing the components in each ordered pair results in a relation that is not a function. A) {(0, 2), (0, 3)} B)

  2. Hisrory

    In Cooperative Federalism A. relations between the states and national government are characterized as hostile. B. there is a strict separation between the states and the national government. c. relations between the states and

  3. human relations

    A major obstacle to developing good human relations skills is that A.human relations aren't rewarding. B. Few persons have common interests. C. Common interests wont help to keep a conversation going. D.people fear taking risks.

  4. world history

    3. How did the Soviet Union respond to the normalization of relations between China and the United States? (1 point)Brezhnev invited Nixon to visit Moscow. Soviet companies set up a thriving trade with China. The Soviet Union cut

You can view more similar questions or ask a new question.