Laurey
This page lists questions and answers that were posted by visitors named Laurey.
Questions
The following questions were asked by visitors named Laurey.
Justifying your conclusions (you could also use examples in order to illustrate your results). What can you say about the sets A and B if we know that: 1. A ∪ B = A 2. A ∩ B = A Thanks for any helpful replies :)
14 years ago
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 flexible, symmetric, anti-symmetri...
14 years ago
Consider the following relation on R1, the set of real numbers R1 = {(1,1), (1,2), (2,1), (2,2), (3,3), (4,4), (3,2), (2,3)} Determine whether or not each relation is flexible, symmetric, anti-symmetric, or transitive. * Reflexive because the relation con...
14 years ago
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...
14 years ago
Answers
The following answers were posted by visitors named Laurey.
Thank you MathMate for your quick reply! I think I understand it a lot better after your post, but I still feel a little fuzzy. So for R1: Reflexive: x = x Symmetric: x = y, then y = x antisymmetric: x = y and y = x that implies x = y (?) Transitive: x =...
14 years ago
R3: Not Reflexive: x ⊀ x Symmetric: Antisymmetric: Not Transitive: I'm not sure how to justify. . . the xy and 0 is throwing me off. . .can you separate them? If that makes any sense. . .I'm lost. But R2 would be considered an equivalent relation because...
14 years ago
Oh yea I meant to type R1, sorry it was a typo. Thank you for your help MathMate!
14 years ago
So, it is not antisymmetric because 2 ≠ 3, but what would have made it true?
14 years ago
OooOOo. . .thank you so much for all your help.
14 years ago
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 (...
14 years ago
Thank you for the reassurance.
14 years ago