Consider a simple environment where a logical agent needs to determine if a room contains a treasure. The agent has the following knowledge: $$If the room is dark, then the treasure is not visible. $$If the treasure is not visible, then it is not detectable by the agent. $$The room is dark. a$)$ Represent the knowledge using propositional logic. b$)$ Based on the given knowledge, can the agent determine whether the treasure is detectable? Justify your answer with logical deductions.