Let $S = \{1, 2, 3\}$. Select all those that give equivalence relations on $S$.

Question

Q: Let $S = \{1, 2, 3\}$. Each of the following subsets of $S \times S$ gives a relation on $S$.

Select all those that give equivalence relations on $S$.

a) $\{(1, 1),(1, 2),(2, 1),(2, 2),(3, 2),(3, 3)\}$

(b) $\{(1, 1)\}$

(c) $\{(1, 1),(1, 2),(1, 3),(2, 1),(2, 2),(2, 3),(3, 1),(3, 2)\}$

(d) $\{(1, 1),(1, 3),(2, 2),(2, 3),(3, 1),(3, 2),(3, 3)\}$

I'm stuck on this question. I said it was b) but I'm not sure if I'm right.

I would really appreciate your help. Thanks!

Thanks, but i didnt ask for a MathJax tutorial. I think what i wrote is clearly legible. — Jane, Mar 11 '18 at 15:16
-1 for an arrogant comment to being pointed to a MathJax tutorial. — Henrik supports the community, Mar 11 '18 at 15:42
@Henrik aren't you suppose to -1 if the question is bad or doesn't make sense or whatever, not because i was being 'mean' as that has nothing to do with maths. — Jane, Mar 11 '18 at 16:52
@Jane no, being mean is legitimate reason for downvote. This is a forum, so we want nice atmosphere before all. We help each other because we want to help — ℋolo, Mar 11 '18 at 16:56
@Jane: I wasn't calling you mean, I was calling your comment arrogant, there's a difference (and I'm not a native english speaker) and I stand by that statement, you could have chosen just to ignore the link, but you had to say that you found it unneeded. — Henrik supports the community, Mar 11 '18 at 18:46
I apologise in that case. Im sorry @Shaun and to the rest for being so arrogant. — Jane, Mar 12 '18 at 09:21
This should be deleted for complete lack of personal input (just like many other questions by this OP). — Did, Mar 12 '18 at 09:50

score 2 · Answer 1 · answered Mar 11 '18 at 15:40

Answer: none(may be you had done typo while typing options)

a relation which is identity, symmetric and transitive is called the equivalence relation!

Clearly, $(b)$ is not equivalence relation! Since it is not identity relation(clearly you can see $(2,2), (3,3)∉\{(1,1)\}$)

Similarly, $(c)$ is not equivalence relation(as $(3,3)∉$Set)

further, (d) is not transitive! (Since $(2,1)∉$Set) hence not equivalence!

Infact, (a) is also not equivalence! Since it is not symmetric (as $(2,3)∉$set)

1 Answers1