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.

3 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.

Advaith on November 10, 2015

Thanks Naz

Oscar on September 15, 2018

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.