- Problem 3 (6 marks). Use truth tables to determine whether the following argument (logical consequence) is correct - show your work. Premise 1. You exist if you know you exist. Premise 2. If you know you exist then you know something. Premise 3. If you know something then you must exist. Conclusion. You exist. Note: you must use appropriately the following three variables (and no others): ex, ke, ks. - Problem 4 (6 marks). Convert each of the following propositions to an equivalent one in CNF. Use the laws of propositional logic (as shown in the lectures) and show your work. Your answers should be as simple as possible. 1 1. (pq) 2. (pq)(p) 3. (pq)(pq)