We can be sure that at least some halogen lamps are well crafted, because halogen lamps from most major manufacturers...

Nicolette on September 16, 2014

Please explain

The answer is B. However, I do not understand how this matches the reasoning in the argument. When I diagram I do not get parallel results. I chose C, and do not see how it is incorrect.

8 Replies

Melody on September 23, 2014

Let's break down the argument:

"Any item on display at Furniture Labyrinth is well crafted."

PR: ODFL ==> WC
not WC ==> not ODFL

"halogen lamps from most major manufacturers are on display at Furniture Labyrinth."

NOTE: These are a specific type of halogen lamp--those from most major manufacturers. We do not know how many other types there are. Thus, we will write this out "some halogen lamps are on display at Furniture Labyrinth."

P: HL-some-ODFL
ODFL-some-HL

Thus, "we can be sure that at least some halogen lamps are well-crafted."

C: HL-some-WC
WC-some-HL

Remember, we can connect a "SOME" statement to a Sufficient & Necessary statement if the right-hand side variable of the "SOME" statement is the same as the sufficient condition of the Sufficient & Necessary statement. We have this scenario in the above argument, so we can combine "PR" and "P1" as follows:

HL-some-ODFL ==> WC

From this we can conclude: HL-some-WC, which is our conclusion. Our correct answer will have the same exact reasoning as the argument above.

Answer choice (B) states: "We can be positive that there are at least a few disturbing sonnets, given that Melinda has written several different kinds of sonnets; everything Melinda writes is disturbing."

Let's break the argument down.

"everything Melinda writes is disturbing."

PR: MW ==> D
not D ==> not MW

"Melinda has written several different kinds of sonnets;"

P1: MW-some-S
S-some-MW

"We can be positive that there are at least a few disturbing sonnets,"

C: S-some-D
D-some-S

Just as in the stimulus, we have a "SOME" statement whose right-hand side variable is the same as the sufficient condition of the Sufficient & Necessary statement. So, we can combine "PR" with "P1" like so: S-some-MW ==> D to conclude: S-some-MW. Thus, answer choice (B) is the correct answer because it has the exact same reasoning as the argument in the stimulus.

Answer choice (C) states: "We can be sure that Gianna will get at least some good mechanical work done to her car, because she can have her car worked on at any several shops in the city, and every shop is capable of doing good mechanical work."

"every shop is capable of doing good mechanical work."

PR: S ==> CGMW
not CGMW ==> not S

"she can have her car worked on at any of several shops in the city,"

P: S

"We can be sure that Gianna will get at least some good mechanical work done to her car,"

C: some GMW

As you can see, this does not have the same reasoning as the argument in the stimulus. In the stimulus we combine a Sufficient & Necessary statement with a "SOME" statement to properly conclude a "SOME" statement.

This argument does not have a premise that is a "SOME" statement. The sentence "she can have her car worked on at any several shops in the city," is neither a Sufficient & Necessary statement, nor is it a Quantity statement. It's merely a statement of fact that acts as one of the premises.

Hope that clears things up! Please let us know if you have any other questions.

Sadaab on September 20, 2019

I like b but why not e?

on June 6 at 11:06AM

Can you please explain why D is wrong if B is right? They seem very similar.

Skylar on June 14 at 02:37PM

@sadaabrahman, happy to help!

The passage reaches the conclusion that "at least some halogen lamps are well crafted." As we see, this statement comments on only "some" of the lamps. (E) reaches the conclusion that "the cornmeal used at Matteo's Trattoria is healthful and organic." Unlike the passage, (E) is not commenting only on "some" of the cornmeal. This is the key dissimilarity in logic that makes (E) incorrect.

Does that make sense? Hope it helps! Please let us know if you have any other questions!

Skylar on June 14 at 02:44PM

@yckim2180, happy to help!

(D) tells us that "every lake nearby is teeming with healthy fish." Does this mean that there are no unhealthy fish in the lakes? No. It would still be possible to have a lake teeming with healthy fish that also has unhealthy minnows present. We cannot assume that all fish or even some minnows in nearby lakes are healthy. Therefore, (D) is incorrect.

Does that make sense? Hope it helps! Please let us know if you have any other questions!

Itzelth on July 8 at 11:42PM

I'm really unable to grasp exactly why the "halogen lamps from most major manufacturers..." turns into a some when its diagrammed. I've tried walking through Naz's explanation about it but I still can't seem to understand it. Can someone explain this please

Victoria on July 20 at 02:38PM

Hi @Itzelth-Gambia,

Happy to help!

This stimulus is a bit like the missing premise drills from earlier in the course. We have our first premise and our conclusion diagrammed, but it is a bit unclear how we are to diagram the second premise.

P1: Any item on display at Furniture Labyrinth is well crafted.

ODFL --> WC
Not WC --> Not ODFL

P2:

C: At least some halogen lamps are well crafted.

HL - some - WC
WC - some - HL

How do we get to our conclusion? Our first premise is a S&N statement. Therefore, we know that the second premise must include a quantifier to allow us to properly draw our conclusion.

"Halogen lamps from most major manufacturers are on display at Furniture Labyrinth." As we do not know how many other non-major manufacturers make halogen lamps or how many different types of halogen lamps the major manufacturers make, we can rewrite this as "some halogen lamps are on display at Furniture Labyrinth."

We definitely know that all halogen lamps are not on display at the store as there are only lamps from most major manufacturers. We also cannot conclude that most halogen lamps are on display for the reasons I've outlined above. However, we know for sure that at least some halogen lamps are on display.

HL - some - ODFL
ODFL - some - HL

This allows us to use the transitive property to properly draw our conclusion. Remember that the arrow in the S&N diagram must always point away from the quantifier.

HL - some - ODFL --> WC

Therefore, HL - some - WC

Hope this helps clear things up a bit! Please let us know if you have any further questions.

Victoria on July 20 at 02:39PM

Sorry @Itzelth-Gamboa