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Laurey
Questions (4)
Which of these relations on {0, 1, 2, 3} are equivalence relations? Justify the relation(s) that are not equivalent.
R1: {(0,0),
4 answers
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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)}
5 answers
786 views
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
7 answers
2,410 views
Justifying your conclusions (you could also use examples in order to illustrate your results).
What can you say about the sets A
1 answer
401 views
Answers (7)
Thank you for the reassurance.
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
OooOOo. . .thank you so much for all your help.
So, it is not antisymmetric because 2 ≠ 3, but what would have made it true?
Oh yea I meant to type R1, sorry it was a typo. Thank you for your help MathMate!
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
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 = y
