[3 pts] Given the following knowledge base below, can you prove that 1. the unicorn is mythical [1pt]? 2. How about magical[1pt]? 3. Horned[1pt]? Knowledge base: If the unicorn is mythical, then it is immortal, but if it is not mythical, then it is a mortal mammal. If the unicorn is either immortal or a mammal, then it is horned. The unicorn is magical if it is horned. Hint: Do not add unnecessary propositional information, e.g., you do not need 'immortal' propositional variable: it is just 'not mortal'. You can use either modus ponens or resolution for the proof. [3 pts] Prove, or find a counterexample to, each of the following assertions: a. [lpt] Ifa ky or B Ey (or both) then (a A B) FY b. [Ipt] If a F (BAY) then a F B and a FY. c. [1pt] If a # (B Vy) then a F B or a By (or both). [2pts] Any propositional logic sentence (tautology) is logically equivalent to the assertion that each possible world in which it would be false is not the case. From this observation, prove that any sentence can be written in CNF. Bonus [3 pts] Consider the following sentence: [(Food = Party)V (Drinks = Party)] = [(Food A Drinks) = Party]. Is it provable? a. [1pt] Determine, using enumeration, whether this sentence is valid, satisfiable (but not valid), or unsatisfiable. b. [Ipt] Convert the left-hand and right-hand sides of the main implication into CNF, showing each step, and explain how the results confirm your answer to (a). c. [1pt] Prove your answer to (a) using resolution (no credit for MP proof)