Claudie is a daughter of friends of the Merricks, and although she does do some cooking and light housework, she is not a servant. I think there is no suggestion that she is expected to sleep with Patrick, and the Merrick parents would probably be horrified if they knew she effectively suggests it. Also, it is canonical that Patrick struggles with at least some humanities as well as maths. He has trouble with foreign languages, and his Latin also appears to be quite weak.
Lizzzar