1. Academy regulations state "midshipman do not sleep in class". We can model this in propositional logic by asserting that the following formula is true: $\forall m[ \text{isMid}(m) \wedge \text{inClass}(m) \Rightarrow \neg \text{isSleeping}(m) ]$. Given that George is a Mid, i.e. $\text{isMid}(\text{george})$, and that George is in class, i.e. $\text{inClass}(\text{george})$, can we deduce that George is not sleeping? Give a proof!
  2. Using the same regulation: given that Gavin is sleeping and he is in class, prove that he is not a mid ... which presumably means he's the professor!
  3. In a previous homework we had a problem in which there were two sessions for talks and a number of potential speakers. We had to express some constraints on how speakers were scheduled for sessions. One of these constraints was: "Nobody can be scheduled for both sessions." One way to write this is 
    (a1 => ~a2) & (b1 => ~b2) & (c1 => ~c2) & ...
    ... where "a1" meant that Alice was scheduled for session 1, "a2" meant alice was scheduled for session 2, and so on. With first-order logic we can express this with one simple rule! Our objects are the speakers, and we will have predicate in1(·), which is true when the argument speaker is scheduled for session 1, and in2(·), which is true when the argument speaker is scheduled for session 2. So here's the rule: 
    ∀p[in1(p) => ~in2(p)]
    Your job: Given the above rule, and given that Anuj is in session 2 or Ben is in session 2, and given that Anuj is in session 1, prove that Ben is not in session 1.