# What does it mean to calculate a relation's quotient set (the set of all of equivalence classes)?

The set in question: T = {(a,a),(b,b),(c,c)}.

I am confused what it means by this, and I haven't found any resources online that helps explain this to me well enough. Any help is much appreciated.

• Welcome to Math Stack Exchange. The quotient set is the set of equivalence classes. In your case, assuming T is the relation for the set {a,b,c}, nothing is related to anything else, so the quotient set consists of singletons Apr 17, 2019 at 13:29
• To consider the quotient you need an equivalence relation(Probably $T$) and a set. If we assume the set was $\{a,b,c\}$ then the quotient is $\{[a],[b],[c]\}$ cause they do not relate with anyone but themselves. Apr 17, 2019 at 13:30

Given a set such as $$S=$${$$a,b,c$$} and an equivalence relation on it, such as $$T$$,
the equivalence class of an element, say $$a$$, is the set {$$x\in S|(a,x)\in T$$} of what is related to $$a$$.
For the relation $$T=$${$$(a,a),(b,b),(c,c)$$}, the equivalence class of an element, say $$a$$, is simply {$$a$$}.
($$b$$ and $$c$$ are not related to $$a$$.)
The quotient set of $$T=$${$$(a,a),(b,b),(c,c)$$} is simply {{a}, {b}, {c}}.