What does the square bracket mean when used with binary relation?

Question

I'm confused what the square bracket means when dealing with binary relations.

What does R[A$\cup$B] mean? What does the square brackets around the A$\cup$B mean?

Answer 1

I would say that $R$ is not a function, but a binary relation, and we perhaps define $$ R[A] = \{b \;:\; \exists a \in A, aRb\} $$

Answer 2

$R$ is a set mapping (may not be functional), and the brackets are just brackets.   $R[A\cup B]$ is the set mapped to by the relation $R$ from the union of sets $A$ and $B$.   That is, the image of $A\cup B$.