How to define secure pseudorandom functions?
Consider yourself an adversary. You're given access to an oracle $O(\cdot)$. You're trying to determine if $O(\cdot)$ is actually random or $F'_s(\cdot)$ with some randomly sampled $s$.
a. Consider $O(0^n)$ and $O(1^n)$.
b. Consider $O(0^n)$
In each case, consider some special event $E$. If $O(\cdot)$ is truly random, what is the probability $p$ that $E$ occurs? If $O(\cdot) = F'_s(\cdot)$, what is the probability $q$ that $E$ occurs? Your distinguishing advantage is $|p-q|$.