#19 - Team captain: Winning requires the willingness to

[cpassaro]

Could you please explain June 2009, Sec. 2 (first LR section) Q19 (team captain)?

Thanks so much!
Cara

[Steve Stein]

Hi Cara,

Thanks for your question. In that one, the captain combines two conditional statements to draw a conclusion:
Winning requires cooperation: Winning cooperation
Cooperation requires motivation: cooperation motivation

Combining these, we get: Winning cooperation motivation

So, winning requires motivation, and (the contrapositive) if we have not motivation, we cannot win.

Correct Answer choice C take the same form:
Our party will keep its status only with more money: status raise money
Raising money requires campaigning: raise money campaigning

Combining these: status raise money campaigning

So, status requires more campaigning, and (the contrapositive) if we don't increase campaigning, we cannot retain our status.


I hope that's helpful--please let me know--thanks!

~Steve

[cpassaro]

Thanks. That helps. I think I got thrown off by the "unless" in answer choice C.

[xishao3]

Hi PowerScore,

I noticed with Answer Choice 'C' that in order to correctly choose 'C' as the appropriate answer, we would have had to taken the conclusion of retain status increase campaigning and go the extra step of figuring its contrapositive not increase campaigning not retain status. Failure to go the extra step would have made the conclusion just a restatement of the conditional relationships stated in the premise. Is this extra step of looking at the contrapositive, even if not listed in the answer, something we should always do?

Many Thanks,
Amy

[Adam Tyson]

Yes and no, Amy. The contrapositive of any conditional statement is logically equivalent to the original claim. That is, they mean the same thing as each other, and are completely interchangeable. In that sense, taking the contrapositive isn't really an extra step, it's just recognizing that you can say the same thing two different ways.

Then again, it still requires recognizing that what you are looking at is a contrapositive, so in that sense you do need to sometimes take that extra step, and when dealing with conditional statements you should always give consideration to the contrapositive.

One thing to keep in mind is that our method of using the "Unless Equation" is not the only way to handle the "unless" in the correct answer choice. There are those folks out there that choose instead to diagram "unless" as meaning the same as "if not", negating it and using it as a sufficient condition. Approached that way, answer C gets diagrammed from the start as:

Campaign Retain Status

and there's no need to think about a contrapositive. We at PowerScore prefer our method, especially when the statement includes a multi-conditional "and" or "or" statement, but neither method is right or wrong, just different.

Short version: contrapositives are identical in meaning to the original conditional claims, so you can always use either one, and should always remain aware of that.

Keep up the good work!

[brcibake]

For the last sentence in this stimulus, I diagrammed
win -> motivation
Why is this not correct?

[Adam Tyson]

You have a mistaken reversal there, brcibake, and the key is the sufficient condition indicator word "if" in the conclusion (the last sentence of the stimulus). "if you are not motivated" tells us that the sufficient condition is motivated, and the other term in the relationship (win) must be the necessary condition. Remember that the order in which the statement are presented is irrelevant - what matters is the logical relationship, which can often be determined by analyzing key language. That sentence could have just as easily been written as "if you are not motivated you will not win" and the meaning would be unchanged.

Study those key indicators to be sure that you are keeping your sufficient and necessary terms straight! That way will lead to consistent success with conditional arguments.

[cmnoury1221]

Hello,
Is answer choice D a mistaken reversal?
Thanks!

[Paul Marsh]

Hi Carolyn! Yes, the conclusion of answer choice (D) is a Mistaken Reversal, so it's an incorrect answer.

The premises in the stimulus follow this following pattern:
A B
B C
Then conclusion of the stimulus takes the contrapositive of those two conditionals chained together, like so:
C A

So we're looking for an answer choice that follows the same pattern: with two conditionals as premises (making sure the necessary condition of one conditional is the same as the sufficient condition of the second conditional), and then a conclusion that chains them together and takes the contrapositive. Let's look at answer choice (D):

The premises look good, right in line with our stimulus:

Repair bicycle Enthusiastic

Enthusiastic Mechanical Aptitude

But then for the conclusion to match the stimulus, we would want to chain the two conditionals together and take the contrapositive. Chaining the two conditional in the premises of answer choice (D) together, we get

Repair bicycle Mechanical Aptitude.

And the contrapositive of that would be

Mechanical Aptitude Repair bicycle

However, the conclusion of (D) instead says

Repair bicycle Mechanical Aptitude

So it's a Mistaken Reversal. Nice going!

[ToadKing]

Hi,

In the stimulus, the contrapositive is given as the conclusion, but in (C) they just straight up give say that S -> C. I didn't want to choose it because on past PTs like PT51 LR1.20 ("Only experienced salespeople will be able to meet the company’s selling quota...") the answer has to 100% match the structure of the stimulus.

Am I thinking about this incorrectly, or are contrapositives alright in parallel questions?