Q21 - The companies that are the

[unprocessed1]

I can easily get it down to A and C, but I've have a lot of trouble seeing why A is wrong and why C is right, the formal logic is seriously confusing me. I'd appreciate the help!

[ManhattanPrepLSAT1]

I'd be happy to help with the conditional logic on this one. And you're right, this one is full of conditional logic.

This is a sufficient assumption question. Meaning, we are asked to fill in the gap in the argument.

The evidence...

1. The companies that purchase software will not buy the software if the costs of training are high.

CH ---> ~B
(CH = costs high, B = buy the software_

2. It is expensive to teach people software that demands the memorization of unfamiliar commands.

MC ---> CH
(MC = memorization of commands, CH = costs high)

The conclusion...

To be successful, commercial computer software cannot require users to memorize unfamiliar commands.

S ---> ~MC
(S = successful, MC = memorization of commands)

and put together...

CH ---> ~B
MC ---> CH

=======
S ---> ~MC

if we take the contrapositive of both premises...

B ---> ~CH
~CH ---> ~MC

========
S ---> ~MC

the gap in this argument is

S ---> B

We can see this buy adding S ---> B to the evidence...

S ---> B
B ---> ~CH
~CH ---> ~MC
=========
S ---> ~MC

where green represents the assumption, blue represents the evidence, and red represents the conclusion drawn.

The statement in green is best expressed in answer choice (C). Answer choice (A) is backwards... It's a classic case of mistaking a sufficient condition for a necessary condition!

Does that help clear things up on this one? Let me know if you still need help with this one.

[sumukh09]

For sufficient assumption questions how do you figure out what the gap in the argument is before going through answer choices? Moreover what missing connection are we looking for when breaking down an argument using conditional logic? Also, you took the contrapositives of the premises and conclusion for this question - is that just by your instincts or is it necessary to do everytime when solving a question using conditional logic?

[WaltGrace1983]

The statement in green is best expressed in answer choice (C). Answer choice (A) is backwards... It's a classic case of mistaking a sufficient condition for a necessary condition!

Just so I am clear...

If the conclusion is the following:

Successful → ~Memorize Unfamiliar Commands

Then, our correct answer, if it is incorporating the term "successful" (which it should because it is the come-from-nowhere, out-of-left field conclusion that incorporates a new word), can only look like the following?:

Successful → _____________________

or

__________________ → ~Successful?

(A) would have been right if it said, "If prime purchasers of computer software don't buy a software product, that product will be unsuccessful"

This is because our chain of logic looks like this:

Unfamiliar → High Cost → ~Buy
Unfamiliar→ ~Successful

If the conclusion gives us (Unfamiliar), then we know (High Cost), and then we know ~(Buy). However, how do we get to ~(Successful)? We have to assume that having a (High Cost) leads to ~(Successful) or ~(Buy) leads to ~(Successful).

[christine.defenbaugh]

Great question, WaltGrace1983!

That's a correct assessment of this question, yes. If the conditional conclusion has a trigger that's never been discussed in the premises, and you're looking for a sufficient assumption, you can be pretty darn sure the correct answer has to have that new-item trigger as a trigger itself.

The negated new-item as the 'result' of a conditional works, just because that's the contrapositive!

However, it might be more useful to think of this in a somewhat broader way that can apply to all sufficient assumption conditional conclusions: you're always looking for the missing link between the trigger and the result of that conditional conclusion.

So, let's consider if your argument looked something like this:


Your conclusion is A-->E, and you want to make it work (Sufficient Assumption), so you have to figure out a way to get all the way from A to E. Imagine they are two islands, and you want to drive from one to the other - so you have to find bridges that get you there. There's not a direct bridge from Island A to Island E, so we have to work with smaller bridges. Fortunately, we have a lot of smaller bridges in play. Any bridge that starts at A and goes somewhere might be useful, and any bridge that ends up at E could be useful too.


You can see that the missing link here is C-->D. If we had that, we could drive all way from A to E, no problem!


Our situation in THIS question looks a bit different (and I've changed the fake premises to reflect that), but we're actually doing the SAME EXACT THING!

We still want to build that bridge from A to E, and any bridge that does part of the job will help:


Now, we're still looking for the missing link! The missing link just happens to be the very first link.


That missing link might also have ended up being the very last link! No real difference in our process! So, while everything you said about what you're doing is essentially correct, I think it's more useful to realize that all Sufficient Assumption questions with conditional conclusions can be broken down the same essential way regardless of where the missing link is.

What do you think?

[ncesomonu]

I have a huge conditional diagramming question.

1. The companies that purchase software will not buy the software if the costs of training are high.

CH ---> ~B
(CH = costs high, B = buy the software_

2. It is expensive to teach people software that demands the memorization of unfamiliar commands.

MC ---> CH
(MC = memorization of commands, CH = costs high)

mattsherman, why did you diagram this relationship like this? In other words why is MC in the sufficient and CH in the necessary? I had it diagrammed as CH----> MC


Please, help me out!

[uhdang]

So, essentially, two main conditional statements are:
1) Buying => ~ Cost High => ~ Requiring Memorization
2) Successful => ~requiring Memorization.

C connects these two with "Successful => Buying" -- "will not be successful unless prime purchaser buy it."

What would happen if there is an answer choice of "Buying => Successful"?
Is that also a correct answer?

[rinagoldfield]

Thanks for your post Uhdang! The two conditional statements you wrote out are perfect. We ultimately need to connect Success--> Buy to make a complete chain. Buy --> Success would not be sufficient, since it reverses the logic that we need. In, fact, incorrect answer choice (A) offers exactly that conditional!

[smsotolongo]

Can someone please explain the diagramming of the second premise? I had it backwards. Can someone please explain why it's diagrammed the way it is?

[uhdang]

Can someone please explain the diagramming of the second premise? I had it backwards. Can someone please explain why it's diagrammed the way it is?

1st Premise: Cost High => ~ Buy
2nd Premise: Educating Memorization => Cost High

Combining these two, you get: Educating Memorization => ~Buy

It's Contrapositive would be: Buy => ~Educating Memorization.
Conclusion read : Successful => ~Educating Memorization.

So, what we need as an assumption here is: Successful => Buy, which is what C is.

Hope this helps.

[HansolL655]

I have a huge conditional diagramming question.

1. The companies that purchase software will not buy the software if the costs of training are high.

CH ---> ~B
(CH = costs high, B = buy the software_

2. It is expensive to teach people software that demands the memorization of unfamiliar commands.

MC ---> CH
(MC = memorization of commands, CH = costs high)

mattsherman, why did you diagram this relationship like this? In other words why is MC in the sufficient and CH in the necessary? I had it diagrammed as CH----> MC


Please, help me out!

Hey there,

Perhaps I can help. I originally also flipped the sufficient and necessary condition for this.

The clue comes from "It". As the subject of the sentence, what does it refer to? It refers to the "software package that demands the memorization of unfamiliar commands." In other words, this sentence:

"It is expensive to teach people a software package that demands the memorization of unfamiliar commands."

is equivalent to:

"A software package that demands the memorization of unfamiliar commands is expensive to teach people ."

Which is easier to see as MC ---> CH

Hope that helps!