Clarify why C

Let's diagram this: At a gathering at which bankers, athletes, and lawyers are present: "All of the bankers are athletes" P1: B ==> A not A ==> not B "none of the lawyers are bankers." P2: L ==> not B B ==> not L Your mistake came in diagramming "P2." P2 has the same structure as "No A is B." We diagram this "If A then not B," i.e. A ==> not B. Think of it this way: no cats are dogs. If you were to diagram that like so: not C ==> D then that would read: "If you are not a cat, then you are a dog." Well, a frog is not a cat, but it is not a dog. So instead, you need to diagram it "If you are a cat, then you are not a dog," since cats can't be dogs. Do you see? Thus, we can combine P1 and the contrapositive of P2 using the rule that states that we can combine two Sufficient & Necessary statements that have the same sufficient condition to make a "some" statement with their respective necessary conditions. For example, if we had: A ==> B and A ==> C, we could conclude that B-some-C. So we can combine P1 and the contrapositive of P2--since they both have "B" as their sufficient conditions--to conclude: "A-some-not L," i.e. answer choice (C): "Some of the athletes are not lawyers." Hope that clears things up! Please let us know if you have any other questions.

Thanks Naz

What lesson did we learn the following S & N rule in? Quantifiers? I can't seem to find this rule of combining to S & N conditions to make a some statement if they share the S in any of the books. I just want to look back and see what other S & N rules I may have overlooked.