# At a gathering at which bankers, athletes, and lawyers are present, all of the bankers are athletes and none of the l...

Nicolette on September 25, 2014

Clarify why C

I am not clear on this answer. When I diagram the information I get the following: B - >A No L - >B This chain of events produces the following: No L - >B, all B - > A So, No L - > A. This matches answer choice E. Yet, C is the correct answer choice? C is not S&N, but quantifiers, as well. I do not see how it is more correct.

Replies

Melody on September 26, 2014

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.