Problem 1: Logic & Truth Tables Consider the strange commute of Zeke. He dislikes getting wet the most and wears a rain jacket to avoid it. But if he were to stay dry without the jacket, he'd prefer to not wear it. A few things will get Zeke wet on his commute. If he's not taking the car (that is, he's riding his bike) and its raining, then he'll get wet. Alternatively, sometimes the neighborhood kids are out with water guns and will certainly shoot water at Zeke. Using the following propositions: K = the neighborhood (k)ids are out with water guns v an W = the (w)eather today is rain C = Zeke is commuting by (c)ar today (assume he commutes by bike otherwise) J = Zeke should wear a rainjacket A) Construct a truth table for J in terms of K, W, C: B) Write an expression for J in Conjunctive Normal Form in terms of K, W, C C) Write an expression for J in Disjunctive Normal Form in terms of K, W, C D) Simplify either of the above expressions (they're logically equivalent) E) Design a circuit which implements your simplified expression