Answer
a) $b_{n}$ is convergent and $a_{n} > b_{n}$ then we cannot conclude.
b) $b_{n}$ is convergent and $a_{n} < b_{n}$ then we can say that $a_{n}$ is convergent as well
Work Step by Step
a) If $a_{n}$ is bigger than $b_{n}$ we cannot conclude anything as it could be anywhere between $S_{b}$ and $\infty$. So if $b_{n}$ is convergent and $a_{n} > b_{n}$ then we cannot conclude.
b) If a series ($b_{n}$) is convergent than we can say that it's sum is smaller than infinity ($S_{b}$ is a real number). This means a series ($a_{n}$) with a sum smaller than $b_{n}$ will be smaller than infinity as well so $a_{n}$ is convergent.
