No member of the Richardson Theater Group is both a performer and an administrator. Since Leon and Marta are both me...

Naz on January 3, 2014

The first sentence is a "not both" sentence. Thus we diagram it:

If a performer, then not an administrator.

P1: P ==> not A
A ==> not P

Then we are told that neither Leon nor Marta is an administrator.

P2: not A

The argument then concludes that they must both be performers.

C: P

This argument is obviously flawed. It takes the necessary condition of the general principle: not A, and uses it to conclude the sufficient condition: P. Remember, don't just reverse! You must reverse AND negate.

Answer choice (C) uses similar flawed reasoning.

"No company can have its headquarters in both Canada and Mexico." Again we have a "not both" premise.

If Canada, then not Mexico.

P1: C ==> not M
M ==> not C

Neither company has it headquarters in Mexico.

P2: not M

Therefore, they both have headquarters in Canada.

C: C

Answer choice (C) takes the existence of the necessary condition (i.e. not M), to prove the existence of the sufficient condition (i.e. not C). Don't just reverse!

Hope that was helpful! Please let us know if you have any other questions.

Ceci on November 6, 2018

why not D? I thought it followed the exact same reasoning?

Mehran on November 11, 2018

Hi @Ceci, thanks for your post. It may help to review the information in the explanation previously posted by @ Naz. We are told that, as far as the Richardson Theater Group is involved, no one is both a performer and an administrator. This is a "not both" sentence, that is diagrammed as:

If a performer (P) then not an administrator (A):
P ==> not A
A ==> not P

We are then told that neither Leon nor Marta is an administrator: not A.

The argument then concludes that both Leon and Marta must be performers (P).

This argument is flawed: it takes the necessary condition of the general principle (not A) and uses it to conclude the sufficient condition (P). That is an incorrect reversal.

Let's look at answer choice (D): No corporate attorney represents both the Dumone Co. (DC) and the Tedenco Co. (TC).
DC ==> not TC
contrapositive: TC ==> not DC

Since Ms. Tseung is a corporate attorney who represents the Dumone Co. (DC),
it follows that she does not also represent the Tedenco Co (not TC).

This is not a flawed argument. There is no incorrect reversal. Rather, the information establishes the sufficient condition with respect to Ms. Tseung (she represents the Dumone Co.), and then concludes that she therefore does not represent Tedenco (the necessary condition: not TC).

Hope that helps. Please let us know if you have any additional questions.