#23 - If the prosecutor wanted to charge Frank with

[Administrator]

Complete Question Explanation

Parallel Flaw—SN. The correct answer choice is (C)

This stimulus presents a conditional argument that begins with the straightforward statement that “if the prosecutor wanted to charge Frank with embezzlement, then Frank would already have been indicted.” We can diagram this as:


PWCFE = prosecutor wanted to charge Frank with embezzlement
FIE = Frank would already have been indicted

Sufficient Necessary

PWCFE FIE

and its contrapositive:

FIE PWCFE


However, we learn that Frank has not been indicted (FIE). Because this evidence triggers the contrapositive, we expect the conclusion would be that the prosecutor does not want to charge Frank with embezzlement (PWCFE), the contrapositive’s necessary condition. But it is not. Instead, the author concludes that Frank is not an embezzler. This conclusion is flawed, because it introduces a new term, which we could shorten to FE, that was not part of the conditional argument, and is therefore without support.

We learn from the question stem that this is a Parallel Flaw question. Our prephrase is that the correct answer choice will have a flawed pattern of reasoning similar to what we saw in the stimulus.

Answer choice (A): Because the conclusion in this answer choice and the conclusion in the stimulus do not match, we can say this choice fails the Match the Conclusion test. In the stimulus, the conclusion is a statement about Frank—“he is not an embezzler”—that can viewed in two ways. Either it is a present tense statement describing Frank, or it can be viewed, by inference, as a statement about Frank’s past actions, i.e., he did not embezzle. However, the conclusion in this answer choice is a statement regarding what Rosita knew in the past. Additionally, this argument is flawed because the conclusion results from a Mistaken Reversal, which does not match the flawed reasoning in the stimulus. We can diagram this choice as:


RNAC9 = Rosita Knew her 9:00 appointment would cancel
RW10 = Rosita would come into work until 10:00

Premise: RNAC9 RW10

Premise: RW10

Conclusion: RNAC9


Answer choice (B): This choice also fails the Match the Conclusion test, because its conclusion is a prediction regarding the future. And, this choice displays a Mistaken Negation, which we can diagram as:

BWL = Barry won the lottery
BSH = Barry would stay home to celebrate

• Premise: BWL BSH
  
  Premise: BWL
  
  Conclusion: BSH

Answer choice (C): This is the correct answer choice, because it contains a flawed argument most similar to that in the stimulus. We can diagram this argument as:


MBLO = Makoto believed he left the oven on
MRH = Makoto would rush home
MLO = Makoto left oven on

• Premise: MBLO MRH
  
  Premise: MRH
  
  Conclusion: MLO

Answer choice (D): This answer choice fails the Match the Conclusion test, because it makes a prediction about what is going to occur. Also, the second sentence indicates the argument will commit a Mistaken Reversal, but then the conclusion introduces a new, unsupported term. While this shift is similar to what occurred in the stimulus, an important difference is that the stimulus led us to believe its conclusion would result from the contrapositive, not a Mistaken Reversal. We can diagram this answer choice as:


TBGP = Tamara believed she was getting a promotion
TCWE = Tamara would come in to work early
TGP = Tamar is getting a promotion

• Premise: TBGP TCWE
  
  Premise: TCWE
  
  Conclusion: TGP

Answer choice (E): As with answer choice (D), this choice fails the Match the Conclusion test, because its conclusion is a prediction about the future. Notice how effective the Match the Conclusion test has been in this question. By using that test, we were able to knock out all four of the incorrect answer choices. While we also diagrammed the conditionality in each choice, that step was not necessary. By using the Match the Conclusion test, we can aggressively slice through the answer choices and move on to the next question.

This answer choice is also incorrect because the pattern of conditional reasoning in this answer choice is flawed in a manner other than what we saw in the stimulus. Here, the second premise is a new term, rather than the new term being introduced in the conclusion, as occurred in the stimulus. We can diagram this choice as:


LBF = Lucy believed she was going to be fired
LCW = Lucy would come in to work today
LF = Lucy is going to be fired

• Premise: LBF LCW
  
  Premise: LF
  
  Conclusion: LCW

[Mmjd12]

Hi there,

For exercise, I am attempting to find the valid contrapositive of the statement “if the prosecutor wanted to charge Frank with embezzlement, then Frank would have already been indicted.”

I landed on “ it is NOT true that if the prosecutor wanted to charge Frank with embezzlement, then Frank would have already been indicted.”

But at first I wanted to go with the statement “if the prosecutor did NOT want to charge Frank with embezzlement, then Frank would NOT have already been indicted” I know this is not the valid contrapositive statement, but I can’t explain the reasoning why.

[Luke Haqq]

Hi Mmjd12!

Let's start with a generic conditional statement:

A B

To take the contrapositive of this, you negate both of the variables and switch their place. So you'd have:

B A

Using the sentence you provided, the original is:

Prosecutor wanted to charge Frank would have been indicted

Negated and flipped around, we'd have:

Frank would have been indicted Prosecutor wanted to charge

In other words, if it is not the case that Frank would have been indicted, then it is not the case that the prosecutor wanted to charge him with embezzlement. Or more succinctly, if Frank hasn't already been indicted, then this must be because the prosecutor did not want to charge him with embezzlement.

[Mmjd12]

Completely understand now, thanks so much.