I assume that this statement applies for specific values of $x,y$ because I'm not sure that (b) or (c) is possible for all $x,y$. Also, the way you've written it here these must be discrete random variables (e.g. by use of the '=') so these are actually pmfs, not pdfs. That being said, first note that $P(X = x, Y = y) = P(X = x | Y = y) P(Y = y)$ (and similarly with the roles of $X$ and $Y$ reversed). So:
(a) implies that $P(X = x | Y = y) = P(X = x)$, which is the definition of independence. That is, knowing that $Y = y$ tells us nothing about the event $X = x$.
(b) implies that $P(X = x | Y = y) < P(X = x)$, which tells us that knowledge that $Y=y$ decreases the probability that $X=x$, meaning that the events $X=x$ and $Y=y$ are negatively ''associated'' with each other (I do not use the term correlation here because that is a statement about two random variables, but the problem stated here is one about probabilities of specific events).
Similarly, (c) gives an indication that $X=x$ and $Y=y$ are two events that are positively associated in some sense.