3. Three CSCI 170 professors are seated in a restaurant, the hostess asks them: "Does everyone want coffee?" The first professor says: "I do not know." The second professor then says: "I do not know." Finally, the third professor says: "No, not everyone wants coffee." The hostess comes back and gives coffee to the professors who want it. Who did she bring coffee to, and why? 4. First, identify the atomic propositions, then translate the premises and conclusion of the following argument into propositional logic. Finally, prove (using rules of inference and propositional equivalences) or disprove (via counter-example) the validity of the argument. - Premise: It will rain or it will snow, or possibly both. - Premise: If it snows, it must be cold. - Premise: It will not rain. - Conclusion: It must be cold