I'm studying set theory and on one exercise on binary relations it asks to find some sets, but I can't find the definitions anywhere. The exercise is:
Let R = $\{< \emptyset,\{\{\emptyset\}\} >,<\{\emptyset\},\{\emptyset\}>, <\{\emptyset,\{\emptyset\}\},\emptyset> \}$ Find: R($\emptyset$), R($\{\emptyset\}$), R ${\emptyset}$,R $\{\emptyset\}$.
I haven't found any definition of R(A) for a set A, neither one of R A(the latter seems strange and I think it could be a typo). For the former, I've thought that it could be R($\emptyset$)= $\{\{\emptyset\}\}$ but it could also be R($\emptyset$) = $\{\emptyset,\{\emptyset\}\}$. Any ideas on the definitions?
Well, $R(A) = \{b\mid (a,b)\in R \mbox{ for some } a\in A\}$ is some common notation. Using this, you can find $R(\emptyset)$ and $R(\{\emptyset\})$.