What does the $/$ symbol in $S/R$ mean, where $S$ is a set and $R$ is a relation?

Question

The '$/$' symbol. Or in another way, if I am asked to 'find $S/R$', what does that mean?

I tried to search for this for searching for notation on Google mostly brings up irrelevant results.

Answer 1

A Quotient Set, eg $S/R$, is the set of all equivalence classes over the set $S$ defined by the equivalence relation $R$.

$$S/R = \big\{[x]_R:x\in S, [x]_R=\{y\in S: \langle x,y\rangle\in R\}\big\}:$$