Every brick house on River Street has a front yard. Most of the houses on River Street that have front yards also hav...

KhoalaBear on August 2, 2015


Can you explain why the answer is not A?

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Naz on August 13, 2015

Let's diagram the argument:

"Every brick house on Rover Street has a front yard."

P1: BHRS ==> FY
not FY ==> not BHRS

"Most of the houses on River Street that have front yards also have two stories."

Q1: FY-most-TS

"So most of the brick houses on River Street have two stories."

C: BHRS-most-TS

We know that we cannot combine P1 and Q1 because to combine a Sufficient & Necessary statement with a Quantifier statement, the right-hand-side variable of the Quantifier Statement and the Sufficient Condition of the Sufficient & Necessary Statement must be the same. We do not have this here. The argument is erroneously combining P1 and Q1, so we must find an answer choice that does the same.

Answer choice (A) is diagrammed like so:

"Since all legislators are politicians"

P1: L ==> P
not P ==> not L

"Most legislators have run for office."

Q1: L-most-RO

"we could conclude that most politicians have run for office."

C: P-most-RO

We can actually combine P1 and Q1 here like so: RO-some-L ==> P to conclude RO-some-P, i.e. some people who run for office are politicians. The issue in this answer choice is that the conclusion uses a "most" when it should use a "some." This is not the same flawed reasoning as the argument.

Therefore, answer choice (A) is not the correct answer.

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

LizD on September 4, 2018

Could you also diagram D as well?

Max-Youngquist on September 5, 2018

@lizd for (D) we have:

"All legislators are public servants"
L ==> PS
Not PS ==> not L

"Most public servants have not run for office"
PS - most - NRO
NRO - some - PS

"Therefore most legislators have never run for office"
L - most - NRO
NRO - some - L

You can how (D) is analogous to the argument in the passage by making the following substitutions:

FY to PS

I hope that helps!