(1) You have constructed an intelligent knowledge-based system which answers queries by drawing conclusions from its knowledge base. Information is stored as predicate logical statements. The system has access to all necessary rules of inference, and can use them to draw solutions. After some training, the system has the following knowledge base: (i) Every student must join at least one of the following clubs: (i) Dance club (ii) Aerobics club (ii) Every student is either in cooking club or they are not in aerobics club (or they are both in cooking and not in aerobics). (iii) If a student is in the Bowling club, they cannot join the Cooking club. (iv) If any student not join the Bowling club, then they must have joined the Football club. (v) No student in the Football club failed to join the Gardening club. (vi) The student Hermoine is not in Dance club. (la) For each of (i)-(vi) above, translate the English sentence of the knowledge base of the club into propositional functions. (1b) Your system is now queried with "Are all students in the Bowling club?" What does it conclude, and why? Include a full logical equivalence proof of your system's answer. (1c) Your system is now queried with "What clubs did Hermoine join?" What does it conclude, and why? Include a full logical equivalence proof of your system's answer.