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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.

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    $\begingroup$ 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 $\endgroup$ Apr 17, 2019 at 13:29
  • $\begingroup$ 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. $\endgroup$
    – Phicar
    Apr 17, 2019 at 13:30

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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 is the set of all equivalence classes.

The quotient set of $T=${$(a,a),(b,b),(c,c)$} is simply {{a}, {b}, {c}}.

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