Final answer:
The correct synonym for 'undermine' is 'drain,' as it also conveys the idea of weakening something in a subtle way.
Step-by-step explanation:
The synonym of "undermine" is a) Drain. The word 'undermine' typically means to weaken or damage something, often in a gradual or stealthy way. The correct synonym among the options given is 'drain,' which can also imply reducing strength or efficacy in a way that's not immediately obvious. The other options signify the opposite or unrelated concepts; 'strengthen' means to make stronger, 'enhance' means to improve, and 'illuminate' means to light up or clarify.