PT68.S3.Q24 - in the riverview building

satyammerjalsat

I am not sure why answer choice D in question 68 section 3 of PT 68 is incorrect. Here is an explanation for why I think D can be considered the correct answer.

I made 3 assumptions about parallel reasoning questions which I would like to explain with aid of the following (flawed) reference argument:
Premises: 1. A --> B
2. A --> C
Conclusion: B -->C


Assumption 1) Contrapositives are permitted and do not change the structure of parallel reasoning question. For example, the following argument would be considered parallel to the reference argument:
Premises: 1. not B --> not A (this is a contrapositive of A -->
2. A --> C
Conclusion: not C --> not B (this is a contrapositive of B --> C)

Assumption 2) Swapping a given variable with its negation at every single occurrence of the said variable does not change the structure of the argument. This is because any variable can be redefined to be the negated version of its original definition. For instance, instead of defining D = dog, we can define D = not dog and then swap every single occurrence of D and not D in the argument without affecting its structure.
For example, the following would be considered parallel to the argument stated above (in assumption #1) and thus, by extension, also to the reference argument:
Premises: 1. not B --> A
2. not A --> not C
Conclusion: C --> not B
Note that I swapped A and not A as well as C and not C from the example in assumption #1.

3) The positioning of the premises is irrelevant to the structure of the argument and thus swapping them is permissible. For instance, the following argument would be considered parallel to the reference argument:
Premises: 1. A --> C
2. A --> B
Conclusion: B --> C
I just swapped premises 1 and 2 from the reference argument.

Now, onto the question. Here is how I traced out the argument in the stimulus:
Premises: 1. balcony --> fireplace
2. balcony --> no 1-bedroom
Conclusion: 1-bedroom ---> no fireplace

Replacing words with symbols in the above argument:
Premises: 1. A --> B
2. A --> no C
Conclusion: C ---> no B

Swap C and no C (assumption #2):
Premises: 1. A --> B
2. A --> C
Conclusion: no C ---> no B

Take contrapositive of conclusion (assumption #1):
Premises: 1. A --> B
2. A --> C
Conclusion: B --> C (contrapositive of no C ---> no

Analysis of flaw: one necessary condition leads to another necessary condition. I am going to look for parallel of this in the answer choice.

Now, onto answer choice D. Here is how I traced out the argument in the answer choice:
Premises: 1. cat --> no dog
2. dog --> no fish
Conclusion: cat ---> fish

Take contrapositive of premise #1 and conclusion (assumption #1):
Premises: 1. dog --> no cat (contrapositive of cat --> no dog)
2. dog --> no fish
Conclusion: no fish ---> no cat (contrapositive of cat --> fish)

Swap premises #1 and #2 (assumption #3):
Premises: 1. dog --> no fish
2. dog --> no cat
Conclusion: no fish ---> no cat


Change to symbols:
Premises: 1. A --> no B
2. A --> no C
Conclusion: no B ---> no C

Swap B with no B and C with no C (assumption #2):
Premises: 1. A --> B
2. A --> C
Conclusion: B ---> C

Eureka!!! Exact same structure as the stimulus.
https://7sage.com/lsat_explanations/lsat-68-section-3-question-24/

Sami

@satyammerjalsat Thank you. :DDD