$\text{Erudition}$ means $\text{scholarship}$
So it is $\text{scholarship}:\text{Scholar}$ Scholar has scholarship.
$\Rightarrow$ $\text{steadfast} : \text{mercurial}-$ there is no "has a" relationship.
$\Rightarrow$ $\text{competence} : \text{strict}-$ there is no "has a" relationship.
$\Rightarrow$ $\text{nurse}:\text{doctor}-$ there is no "has a" relationship.
$\therefore$ $\text{skill} : \text{craftsman}$ Craftsman has skill $-$ is the most appropriate choice.
So, option C. $\text{skill} : \text{craftsman}$ is the correct answer.