Need typed solution only

1. Let p and q be the propositions p: It snowed. q: Eve goes skiing. Express each of these propositions using p and q and logical connectives. (a) It snowed but Eve does not go skiing. (b) Whenever Eve goes skiing, it snowed. (c) It having snowed is sufficient for Eve to go skiing. (d) For Eve to go skiing, it is necessary that it snowed. (e) If it didn't snow, then Eve does not go skiing. (f) Whenever Eve doesn't go skiing, it has not snowed. 2. For the propositions in Problem 1, identify all pairs of propositions that are logically equivalent. Justify your answer. 3. State the converse, contrapositive and inverse of the conditional statement: When it's hot out, it is necessary that I eat ice cream. 4. Steve, Bill and Larry go to a bar. The bartender asks: "Does everyone want beer?" Steve says: "I don't know." Bill says: "I don't know." Finally Larry says: "No, not everyone wants beer." The bartender proceeds to serve beer to those among these three who want it. How did he figure out who wanted beer