Is Single-member relation an equivalence

Question

Single-member relation is an equivalence.

For example the relation R={(1,1)}. Is R equivalence relation on a set?

Thanks.

"Is R equivalence relation on a set?" If the set is {1}, yes. Otherwise, it is not. — Did, Oct 13 '13 at 13:23

DanielY · Answer 1 · 2013-10-13T09:54:08.127

0

Not every single-member relation is an equivalence.

Counter-example: $R_2 = ${$(1, 2)$}

edited Oct 13 '13 at 09:54

answered Oct 13 '13 at 09:48

DanielY

So $R_1 = ${$(1, 1)$} is an equivalence? – Wokulmush Woker Oct 13 '13 at 12:16
Yes. But not any single-member relation – DanielY Oct 13 '13 at 12:21
Actually ${(1,1)}$ is not an equivalence relation, except on the set ${1}$. – Did Oct 13 '13 at 13:22
You mean the relation $R_1 = ${$(1,1)$} on set $S = ${$1, 2, 3, 4$} , is not an equivalence? – Wokulmush Woker Oct 14 '13 at 13:05
@wokwok: no it isn't since it doesn't contain $(2,2)$, $(3,3)$, or $(4,4)$. – robjohn Oct 14 '13 at 20:15

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