The Definitive Guide to Sufficient and Necessary Conditions: Part 3

In Part 1 of this guide, we learned what a sufficient condition is and what a necessary condition is, and that a necessary condition is nothing but a reversed sufficient condition. In Part 2, we learned that contrapositives are a way to express that relationship.

In Part 3, we’re going to look at how all this knowledge of conditional logic can help you to navigate through specific Logical Reasoning questions on the LSAT.

Inference Questions

On many inference questions, you are presented with a chain of conditional logic and asked to find an inference from it. Whenever there is a chain, the answer will always be connecting things on the chain that were not explicitly connected. Recall that:

If X is sufficient for Y,

and Y is sufficient for Z,

then X is sufficient for Z.

If Z is necessary for Y,

And Y is necessary for X,

Then Z is necessary for X.

So for example, if the stimulus in an inference question were to say:

W is sufficient for X. X is sufficient for Y. Y is sufficient for Z.

Then, you could infer any of the following three things:

W is sufficient for Z.

W is sufficient for Y.

X is sufficient for Z.

So, in practice, let’s say you got this paragraph:

Marcy’s Coffee is in danger of going bankrupt. However, if it begins the expensive new marketing campaign currently being considered, that would be sure to keep it alive for at least one year. Mr. Young, if promoted to manager of Marcy’s Coffee, will certainly initiate this marketing campaign.

We have a standard causal chain here. If X then Y, and if Y then Z. They were mixed up in the paragraph though, so the structure as written was really…

If Y, then Z. If X, then Y.

…where X = Mr. Young becoming manager, Y = the campaign being initiated, and Z = Marcy’s Coffee surviving at least another year.

Therefore, a correct inference here could be:

If Mr. Young is promoted to manager of Marcy’s Coffee, it will survive for at least another year.

This may seem basic, but often some of the conditions in the paragraph are stated as sufficient and some are stated as necessary, and it’s your job to reverse them all into either sufficient or necessary so that you can chain them up!

For example:

In order for the movie to be good, it has to have good dialogue. The only way for Jerry to express positive emotion is by smiling. If the movie has good dialogue, Jerry will express positive emotion.

Here, we have a necessary condition in the first sentence, a necessary condition in the second sentence, and a sufficient condition in the third sentence! The layout was:

X is necessary for W.

Z is necessary for Y.

X is sufficient for Y.

Reversing the necessary conditions into sufficient conditions and reordering them gets you:

W is sufficient for X.

X is sufficient for Y.

Y is sufficient for Z.

…where W = the movie being good, X = the movie having good dialogue, Y = Jerry expressing positive emotion, and Z = Jerry smiling.

Therefore we can chain everything up from W to Z, and infer that:

If the movie is good, Jerry will smile.

If the movie has good dialogue, Jerry will smile.

…and so on.

Thus, converting between sufficient conditions and necessary conditions is often necessary to create causal chains on trickier inference questions in order to spot the answer.

In general, it is easier to convert everything into sufficient conditions than it is to work with necessary conditions.

Parallel Reasoning Questions

On parallel reasoning questions, you have to convert the initial argument into its skeleton, and then find the answer choice with the matching logical skeleton.

Often, the skeleton will have multiple sufficient/necessary conditions and chain them together for the conclusion. This is something we’ve learned how to do. For example:

On every Sunday, I go for a jog. Every time I go for a jog, I wear my baseball cap. Thus, on every Sunday, I wear my baseball cap.

The skeleton for this argument would be:

If K, then L.

If L, then M.

Therefore, if K, then M.

…where K = it being Sunday, L = me going for a jog, and M = me wearing my baseball cap.

Parallel flawed reasoning questions can be a bit trickier though.

For example, a flawed skeleton that could easily come up on an LSAT is:

If K, then L.

If L, then M.

Therefore, if M, then K.

That incorrectly reverses the direction of the chained M-K relationship. In this case, keeping K, L, and M the same, it would look like this:

On every Sunday, I go for a jog. Every time I go for a jog, I wear my baseball cap. Thus, every time I wear my baseball cap, it’s Sunday.

Remember, it can be ordered differently in the paragraph without the skeleton changing, so if this were a parallel flawed reasoning question, this answer would be a correct one:

If you ate breakfast today, you must have set your alarm last night, since whenever you wake up early, you eat breakfast, and whenever you set your alarm, you wake up early.

A careful reading of this argument shows that the skeleton matches the above one exactly, where K = setting your alarm, L = waking up early, and M = eating breakfast. It’s important to be able to identify two arguments with the same logical skeleton even when they are verbalized in a different sequence.

Having a good handle on necessary/sufficient condition chains will help you a lot on some of the trickier parallel reasoning skeletons.

Assumption Questions

Assumption questions with causal chains can get tricky very quickly, and being able to map everything out and convert between necessary and sufficient can be a huge help!

On assumption questions, you are looking for the missing hole in the argument. When a causal chain is being drawn, you simply need to find the two dots that were not connected explicitly in the argument. I’ll use an example from above and remove one of the conditions:

Marcy’s Coffee is in danger of going bankrupt. However, if it begins the expensive new marketing campaign currently being considered, that would be sure to keep it alive for at least one year. Therefore, if Mr. Young is promoted to manager of Marcy’s Coffee, it will survive for at least another year.

If you follow this chain carefully, you can spot which dots need to be connected. As is, the skeleton is:

If Y, then Z.

Therefore, if X, then Z.

Clearly, therefore, this argument just assumed:

If X, then Y.

…where X = Mr. Young becoming manager, Y = the campaign being initiated, and Z = Marcy’s Coffee surviving at least another year.

Thus, the correct answer, if asked for the missing assumption, would have to be something to the effect of:

Mr. Young, if promoted to manager of Marcy’s Coffee, will certainly initiate this marketing campaign.

(…the sentence I subtracted from the initial argument above.)

Let’s do one slightly trickier one to close this section off!

Listening to classical music often has the effect of calming one’s nerves. Therefore, listening to classical music before bedtime can make it easier to fall asleep, since melatonin promotes sleep, and a reduction in blood pressure is always accompanied by a stimulation of melatonin.

OK, let’s try to chain this up to find the missing link. Try it first on your own.

When you’re ready, here’s what it is (“causes” is synonymous with “is sufficient for”).

A causes B.

C causes D.

D causes E.

Therefore, A causes E.

…where A = listening to classical music, B = calming nerves, C = reduction in blood pressure, D = melatonin, and E = sleep.

Connect everything back to the argument and you’ll see that it matches up!

The point is, if you can do this then the answer becomes clear! What’s the missing link in the above chain? That’s right:

B causes C.

Therefore, the missing assumption would have to be something to the effect of:

Calming nerves has the effect of reducing blood pressure.

Notice how this missing assumption doesn’t mention anything about sleep or classical music! Those parts were neatly tied up – the dots that were left unconnected were buried in the middle of the argument.

The point here is that you can predict that that will be the answer, without even looking at the answer choices!

You will encounter many tricky assumption questions like this with convoluted chains, especially towards the end of a section. Being able to quickly map them out, find the missing link, and predict the answer can transform them into a piece of cake!

For a more in depth look at conditional logic, and a discussion of how it can be applied to logic games specifically, check out my comprehensive LSAT Course.

Oh, and if you haven’t already, download your Free MasterLSAT Study Guide, which will tell you exactly what you need to do to reach a 99th-percentile score on the LSAT.

Happy studying!

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