I don't understand this exercise from the book:
There are $16$ possible different relations $R$ on the set $A=\{a,b\}$. Describe all of them.
Firstly, this is the definition of a relation:
A relation on a set $A$ is a subset $R\subseteq A\times A$.
So in the exercise above, shoudln't $R$ be the subset of $A\times A=\{(a,a), (a,b), (b,a), (b,b)\}$?