Self-study
Team captain: Support Winning requires the willingness to cooperate, Support which in turn requires motivation. ██ ███ ████ ███ ███ ██ ███ ███ ███ ██████████
Use Formal Logic
If thinking about this question in English is easier for you than using formal logic, you need more practice gaining fluency in formal logic. Think of English and formal logic as two closely-related tools, like a hand screwdriver and a power screwdriver. While it’s true that any job you can complete with one you could also complete with the other, they each have niche uses in which they excel. If you find yourself tackling a line of 100 wood screws with a hand screwdriver, you need to get better with the power screwdriver.
Diagramming The Argument
The first sentence combines two claims, both of which use the word requires to indicate the necessary condition:
Premise 1: Winning → Cooperate
Premise 2: Cooperate → Motivation
They make a chain:
Chain 1+2: Winning → Cooperate → Motivation
The conclusion uses if to indicate the sufficient condition:
Conclusion: /Motivation → /Winning
Making sense of the argument requires taking the contrapositive either of the Conclusion or of Chain 1+2. Remember that when we’re evaluating an argument’s structure, logically equivalent translations (like contrapositives) are, in fact, equivalent. So either of these is fine:
(CP) Chain 1+2: /Motivation → /Cooperate → /Winning
Conclusion: /Motivation → /Winning
Chain 1+2: Winning → Cooperate → Motivation
(CP) Conclusion: Winning → Motivation
19.
The pattern of reasoning in █████ ███ ██ ███ █████████ ██ ████ ███████ ██ ████ ██ ███ ████████ ██████
a
Being healthy requires █████████ ███ ██████████ ████████ ████ ██ ███████ ███ ██████████████ ██████ ███ █████ ██ ██ ███████ ████ ███ █████████
Premise 1 matches:
Premise 1: Healthy → Exercise
Premise 2 also matches (we do in fact treat “involves” as “always involves” here):
Premise 2: Exercise → Risk of Injury
But the Conclusion just negates Premise 1’s necessary condition, which is no good:
Conclusion: Healthy → /Exercise
b
Learning requires making ████ █████████ ███ ███ ████ █████ ██ ███ ███ ██ ████████ ██ ███ ████ ███ ████ ████████ ███████ █████ █████ █ ██████████ ████████████
Premise 1 matches:
Premise 1: Learning → Mistakes
Premise 2 looks sketchy, but because the order of claims doesn’t matter, it actually matches just fine – it adds a link to the chain before Premise 1 instead of after.
Premise 2: Improve → Learning
Chain 2+1: Improve → Learning → Mistakes
(B)’s conclusion is the killer:
Conclusion: /Improve → /Mistakes
Perhaps you were caught up by the without phrasing, which negates the sufficient condition. In any event, (B) gives us the inverse of the conclusion we want.
c
Our political party ████ ██████ ███ ██████ ████ ██ ██ ██████ ████ ██████ ███ ███████ ████ █████ ████████ █████████ ████████████ ██ ███ █████ ████ ███ ██████ ███ ██████ ██████ ██ █████████ ███ ████████████
Premise 1 matches, but you’ve gotta get the only if phrasing right. It introduces the necessary condition:
Premise 1: Status → $$$
Premise 2 matches:
Premise 2: $$$ → Campaigning
Chain 1+2: Status → $$$ → Campaigning
The conclusion matches too, but you’ve gotta get the unless phrasing right. It negates the sufficient condition:
Conclusion: /Campaigning → /Status
As with the stimulus, making sense of this argument requires taking the contrapositive either of the Conclusion or of Chain 1+2. Here’s both just for convenience:
(CP) Chain 1+2: /Campaigning → /$$$ → /Status
Conclusion: /Campaigning → /Status
Chain 1+2: Status → $$$ → Campaigning
(CP) Conclusion: Status → Campaigning
d
You can repair ████ ███ ███████ ████ ██ ███ ███ █████████████ ███ ██ ███ ███ █████████████ ███ ████ ████ ████ ██████████ █████████ ██ ██ ███ ███ ███ ████ ██ ██████ ████ ███ ████████ ███ ████ ██████████ █████████
Premise 1 matches, but you’ve gotta get the only if phrasing right. It introduces the necessary condition:
Premise 1: Repair → Enthusiastic
Premise 2 matches using a straightforward “if, then” phrasing:
Premise 2: Enthusiastic → Aptitude
Chain 1+2: Repair → Enthusiastic → Aptitude
(D)’s conclusion is the killer:
Conclusion: /Repair → /Aptitude
That’s the inverse of the conclusion we want. (D)’s conclusion uses the straightforward “if, then” phrasing, so if you picked (D) it’s likely because your original stimulus diagram (or your mental model 🙄🙄🙄) was off.
e
Getting a ticket ████████ ███████ ██ █████ ███████ ██ ████ ████████ █████████ ██ ██ ███ ██ ███ ████ ██ █████ ███ ████ █████████
Premises 1 and 2 match, and use the same “requires” phrasing as the stimulus:
Premise 1: Ticket → Line
Premise 2: Line → Patience
Chain 1+2: Ticket → Line → Patience
(E)’s conclusion, though, gives us the inverse of Premise 2 on an “if not this, then not that” phrasing:
Conclusion: /Line → /Patience