2.5 - Sufficient vs. Necessary

Let's take a closer look at sufficient and necessary. Buckle up for a longer lesson—this is one of the most critical LSAT skills, so I'm going to dive deep.

In this lesson we will:

• Recap sufficient and necessary definitions
• Discuss conditionals that don't use the "if-then" format
• Introduce sufficient and necessary assumptions
• Demonstrate some common ways the LSAT confuses sufficient and necessary

Recap: Sufficient and Necessary Conditions

Recall our working definitions for sufficient and necessary from our last lesson. Sufficient means enough. Necessary means required or inevitable.

A sufficient condition is a trigger that forces the necessary condition to occur.

A necessary condition is the shot fired whenever the trigger gets pulled.

Here's an example: 

If someone's at the door, my dog barks.

This conditional tells us a few things.

1. Any time someone comes to the door, it's guaranteed that my dog will bark.
2. If my dog happens to be barking, I can't be certain that someone's at the door.
3. If my dog isn't barking, I know for sure that someone isn't at the door (the contrapositive).

Other Ways to Introduce Conditionals

Conditional statements aren't always presented in "if-then" format. Sometimes they use different indicator words. Sometimes they're nested in the implications of other conditionals.

Introducing Sufficient Conditions Without "If"

Here are some terms you're likely to see on the LSAT that introduce sufficient conditions without using "if". I've paired them up with an example demonstrating how each term introduces the condition. I've then rewritten each one as an "if-then" conditional to make things crystal clear.

When 

When it rains, the street gets wet.

Here, rain is the sufficient condition. When we have rain, we invariably get a wet street.

Rephrased as an "if-then": If it rains, then the street gets wet.

Whenever

Whenever I study, I learn something new.

Here, studying is the sufficient condition. My studying results in my learning something new.

Rephrased: If I study, then I learn something new.

Every 

Every attendee will get the discount code.

Here, attending is the sufficient condition. Our attendance guarantees we get the discount code.

Rephrased: If you attend, then you will get a discount code.

All 

All biology majors take microbiology.

Here, being a biology major is the sufficient condition. Being a bio major requires us to take micro bio.

Rephrased: If you are a biology major, then you take microbiology.

Any

Any coin minted before 1950 is mostly nickel.

Here, minting before 1950 is the sufficient condition. A coin minted earlier than 1950 guarantees it's mostly nickel.

Rephrased: If a coin is minted before 1950, then it's mostly made of nickel.

Introducing Necessary Conditions Without "Then"

Next, let's look at some terms that introduce necessary conditions other than "then".

Only If 

Johnny will ride bikes only if Erika does too.

This Erika must go riding bikes for Johnny to go riding bikes. Erika riding bikes is required for Johnny to ride bikes. If Erika doesn't go riding, neither will Johnny.

Unless

You won't get desert unless you eat your veggies.

To even have a shot at getting desert, you have to eat the veggies. No veggies? No desert. For sure.

Requires

Earning an Economics degree requires passing macroeconomics.

Got an economics degree? I know you passed macro. How? It was a requirement—a necessary condition of getting your degree.

Must

To have electricity, you must pay your bill.

Having electricity requires paying your bill. At bare minimum, having electricity means you paid your bill.

Depends On / Upon

The project's success depends on a timely launch.

We need a timely launch in order for the project to succeed. If we don't have a timely launch, the project will not succeed.

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These lists aren't exhaustive, so always be on the lookout for triggers (sufficient conditions) and requirements (necessary conditions).

Sufficient and Necessary Assumptions

Next, let's talk assumptions.

On the LSAT, an assumption is an unstated premise in an argument. We're mainly concerned with two kinds: sufficient and necessary assumptions. One guarantees an argument's truth and validity. The other's merely a requirement for the argument to have a shot at being true.

If you've been paying attention, then you can probably guess which is which. See what I did there? 😉

Sufficient Assumptions: Prove the Conclusion

When true, sufficient assumptions guarantee the argument's conclusion. In simpler terms, the argument wins.

Consider this argument:

Premise: Brandon got a 175 on the LSAT.
Conclusion: Brandon will go to law school for free.

Now, imagine I've tasked you with guaranteeing this conclusion. All we need to do is add an assumption to the mix that guarantees I go to law school for free.

For example, adding in "Anyone who scores 175 on the LSAT attends law school for free," would do the trick. But so would "Anyone who takes the LSAT attends law school for free."

In the former example, we get the following: 

Anyone scoring over 175 attends for free → Brandon scored 175 → Brandon attends will go to law school for free.

In the latter example, we get: 

Take the LSAT → Attend for free. 
Brandon's 175 means he took the LSAT → Brandon attends for free.

Just like a sufficient condition is enough to guarantee a necessary condition, a sufficient assumption is enough to guarantee an argument's conclusion.

Later in the course, we'll cover how you can use this framework to predict Sufficient Assumption questions 100% of the time.

Necessary Assumptions: Conclusion Requirements

Necessary assumptions are premises that must be true for a given conclusion to hold. It's a piece of information that the argument depends on or else it falls apart.

Consider this argument:

Premise: Bluejays are no longer seen in our area.
Conclusion: Therefore, bluejays are now extinct.

Now, imagine I asked you to point out something this conclusion depends on. Your job wouldn't be deciding whether the conclusion is absurd. It would be to tell me what else would have to be true for the conclusion to hold any water.

Well, for one, the bluejays better not have migrated to another area. Otherwise, they wouldn't be extinct. This is a necessary assumption. And that "otherwise" bit is an example of something we LSAT nerds call the negation test. We'll dive deeper into this technique in a later lesson.

It's important to note that many arguments have multiple necessary assumptions.

Think back to our bluejays.

Not only must the bluejays not have migrated, but for them to now be extinct like the author says, they better not have any other natural habitats. And there better not be any other evidence of them outside of the them no longer being seen in the area. If either of these additional ideas isn't the case, then the author's conclusion falls to pieces.

Remember, necessary means required or inevitable. Just like a necessary condition is required when its sufficient condition is met, a necessary assumption is required for an argument to have any chance at being true.

Confusing Sufficient and Necessary

The LSAT loves to confuse sufficient for necessary. You can safely assume that your official tests will address it multiple times (often multiple times per section). Here are two common ways the LSAT confuses sufficient and necessary paired up with examples.

Mistaken Reversal

Mistaken reversal screws up a conditional's contrapositive.

This happens when we treat satisfying a necessary condition as if it was sufficient to guarantee the sufficient conditions. In other words, by swapping the sides of a conditional statement without remembering to negate the conditions after swapping them. See the example below.

Original: If it rains, then the street will get wet.
Contrapositive: If the street isn't wet, then it didn't rain.
Mistaken Reversal: The street is wet, so it rained.

The easiest way to deal with this version of confusing sufficient and necessary is to ask yourself about all the different ways the necessary condition might occur without the sufficient condition occurring. In our example, that means all the ways the street got wet without it raining. Maybe a water main broke, or a fire hydrant ruptured, or maybe there was a tsunami. The list goes on, but the point remains: it didn't have to be rain just because the street is wet.

Mistaken Negation

Like mistaken reversals, mistaken negation also screws up the contrapositive. It happens when we negate each side of a conditional statement but forget to swap them. Let's use the wet street example again.

Original: If it rains, then the street will get wet.
Contrapositive: If the street isn't wet, then it didn't rain.
Mistaken Negation: It didn't rain, so the street isn't wet.

Similar to the mistaken reversal example, we can think of numerous ways the street could be wet without it raining. In other words, we took different paths to reach essentially the same flawed conclusion.

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That does it for our deep dive on sufficient and necessary.

Next, we'll take a look at how the LSAT tests our understanding of correlation and causation. See you there!

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