Q9 - To use the pool at the City Gym, one must have a member

[r.gupta88]

Its the day before the exam, i do not know if anyone will get this in time. I am having trouble in diagramming the conditional reasonning here.

Use Pool ---> required membership
Sarah has membership therefore she must use pool

can someone help me diagram and get to the right answer.

I picked D :

[sumukh09]

1. Use pool ---> Need Membership
2. Sarah has a Membership ---> She must Use Pool

B) is just a fancy way of saying that the argument committed a mistaken reversal.

Let's break down B) for a more clear understanding of what it means

"treats a statement whose truth is required for the conclusion to be true" = because it must be true that a membership is required ie) the necessary condition of premise 1, for the conclusion to be true - that is, that Sarah uses the pool occasionally

"as though it were a statement whose truth ensures that the conclusion is true" = as though the necessary condition ensures (or guarantees) that the conclusion is true ie) confuses the necessary condition that a membership is required for a sufficient condition ensuring that she uses the pool at least occasionally

If the above was confusing (and I'm rereading it right now and it confused me a little) then an easier way to understand it would to recognize that the conclusion is a reversal of the conditional logic of the premise which is a flawed method of argumentation called mistaken reversal.

if the premise is A ---> B

then concluding B ---> A is invalid!

Hope this helps, good luck tomorrow (or whenever you take it assuming you are in the Northeast).

[slimz89]

I was actually stuck between B and D but ultimately I chose b. I eliminated D because of of the word "most". This answer choice is commuting it's own flaw in making the same flaw as the passage above. So there is no way that this is describing a mistaken reversal.

[rinagoldfield]

Great conversation above. Sumokh, your explanation is excellent. Slimz89, I’m not exactly sure which answer choice you are are describing as "commuting it's own flaw in making the same flaw as the passage above. So there is no way that this is describing a mistaken reversal," but you’re right to eliminate (D).

But, let’s look back at the question. This is a flaw question, so let’s start with the argument core:

Premises:
If use pool --> member
Sarah is a member

Conclusion:
Sarah uses the pool

As Sumokh writes above, the flaw here lies in the logic reversal. We know Sarah’s a gym member, but this doesn’t mean that she definitely uses the pool. Maybe Sarah has the membership so that she can go to yoga class and use the elliptical machine, but does not know how to swim.

(B) says this, albeit in convoluted language. If the conclusion were true (i.e., if Sarah uses the pool), it would NECESSARILY FOLLOW that Sarah is a gym member. In other words, it would be "required" that Sarah is a member. However, Sarah being a member is not enough to "ensure" that Sarah uses the pool. Again, maybe she just uses her membership for yoga.

(A) bring up exceptions and strict enforcement, which are irrelevant to the argument.

(C) talks about "two alternatives," but no two alternatives are presented.

(D) is kind of twisted, but it really says that the argument "concludes that Sarah uses the pool because she’s a gym member, and most gym members use the pool." However, we don’t know whether most gym members use the pool. So this brings up a new premise that wasn’t in the argument.

(E) also mixes up the argument; the conclusion doesn’t restate any premise.