That K is a relation between X and Y means it is a subset of the Cartesian product \$$X \times Y\$$.

Let \$$f_1: X \rightarrow 2^Y\$$ be the function sending an object \$$o \in X\$$ to the set of attributes which apply to \$$o\$$, i.e.,

\$f_1(o) = \lbrace a \in Y\ |\ (o,a) \in K \rbrace \$

I called it \$$f_1\$$ because it operates on a single object.