4. Use only what we have covered so far in the course. Assume the following: 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. (a) Write the above sentences in propositional logic, using only the propositions: { Horned, Mammal, Mortal, Mythical } (b) Concert the above sentences to CNF. (c) Prove via resolution that the unicorn is mythical. (d) Prove via inference that the unicorn is mythical. (e) Prove via model checking that the unicorn is mythical. (Hint: There should be 16 rows in your enumeration.) 4. Use only what we have covered so far in the course. Assume the following: 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. (a) Write the above sentences in propositional logic, using only the propositions: { Horned, Mammal, Mortal, Mythical } (b) Concert the above sentences to CNF. (c) Prove via resolution that the unicorn is mythical. (d) Prove via inference that the unicorn is mythical. (e) Prove via model checking that the unicorn is mythical. (Hint: There should be 16 rows in your enumeration.)