LRFoundation

Conditional Logic

Conditional Logic Intro

Conditional logic shows up throughout the LSAT logical reasoning sections. You'll often encounter it in Flaw questions, in Must be True and Most Strongly Supported questions (and trap answer choices!), and as the foundation of Sufficient and Necessary Assumption questions.

Conditional logic involves two terms that have a very specific relationship with one another. We call them the sufficient and the necessary conditions, respectively. Consider the following statement:

"If it's rainy, then it's cloudy."

Take a minute to think about it. Which of the above terms is sufficient for (guarantees) the other, and which is needed for the other?

The answer is that rain is sufficient for clouds, and clouds are necessary for rain. After all, rain guarantees that it's cloudy out, right? And you need clouds, or else you can't have rain.

Diagramming

If you've studied the LSAT at all you may have seen someone diagram conditional logic whether in a course, curriculum, or explanation of a question. Diagramming can be a useful way to organize conditional logic in written form. The basic template is as follows:

Sufficient → Necessary

So for the statement "If it's rainy, then it's cloudy," the diagram would look like:

Rain → Clouds

Because rain is sufficient and clouds are necessary.

A note about diagramming: I typically (not always, because every student is different) discourage my students from diagramming. It's not necessary for top percentile LSAT scores (I got a 179 and didn't even really know how to diagram at the time), and it adds complexity and takes up time on an already complicated, time-constrained test. However, I do use it as a teaching aid because it can be an illustrative way to organize and display explanations of conditional logic.

Translating Conditional Logic

In the section above I presented you with a conditional relationship in "if, then" form. This is one of the most common ways of presenting conditional logic and can be translated as "if sufficient, then necessary." Just like in the previous section when we said "if it's rainy (sufficient), then it's cloudy (necessary)."

Here are some common ways that conditional logic is presented on the LSAT and how to translate them. Read through and start to familiarize yourself with the indicator words:

  1. If sufficient then necessary

  2. All indicates sufficient: All dogs are mammals

    Dog → Mammal

    This works for "Any" too: Any dog is a mammal

  3. Only indicates necessary: Only practice leads to mastery of the LSAT

    LSAT Master → Practice

    This works for Only if too: Only if you practice will you master the LSAT

The majority of the time for this indicator word you will see Only or Only if. However, an exceptional case to be aware of is The Only. Consider the following:

"The only way to master the LSAT is practice."

Being an LSAT Master is still sufficient to know that a person practiced, and practice is still necessary for mastery. But now "master" (the sufficient condition) is closer to "only" - what gives? Technically, what follows "only" is "way" - which in this case refers to practice as being the "way" to mastery. So "only" still technically indicates the necessary condition, but the sufficient condition is closer to our indicator word. So make sure to consider the meaning of the sentence as a whole in the rare case that you encounter "the only".

  1. Unless indicates necessary: I won't go to the store unless I need milk

    Store → Need milk

I'm not going to the store unless I need milk - ok, so the only scenario in which I'm going to the store is if I need milk. I need to need milk to go to the store, so needing milk is the necessary condition. And if you see me at the store, what do you know for sure? That I must have needed milk! So me being at the store is sufficient to know that I needed milk.

This works for Until too: We won't take off until the pilot gets here

Take off → Pilot here

The same goes for Without too: Max doesn't eat salad without a fork

Max eating salad → Max using a fork

Note: you negate the part before unless/until/without to get the sufficient condition

  1. The term that follows "No" is sufficient, and then the other term is negated and treated as the necessary condition: No dogs are reptiles
    Dog ->!Reptile

    Note: you can think about "no dogs are reptiles" as "every single dog is not a reptile." All dogs lack the characteristic of being a reptile.

    You could also see "Not" as an indicator word: Dogs are not reptiles
    Dog ->!Reptile

  2. You may also see examples like:

    Being in New Jersey guarantees that you are in the United States:
    NJ → USA

    Anyone from the boss' country club can get the job:
    CC → Able to get the job

    I feel rested whenever I get a good nights sleep:
    Good nights sleep → Well rested

    Humans never have 2 heads:
    Human → !2 Heads

    Construction workers need to wear helmets on the job site:
    CW on job site → Helmet

  3. Lastly, "if and only if" indicates both sufficient and necessary:

    I have a vegetarian diet if and only if I don't eat meat:
    Vegetarian → No meat and No meat → Vegetarian

The Contrapositive

Imagine a day where it's not cloudy. Could it possibly be raining?

Of course not! After all, clouds are necessary for rain. So there's a logical conclusion to be made if you don't have the necessary condition of a conditional relationship - you must also not have the sufficient.

So if we consider the conditional relationship:

Rain → Clouds

Then another logical statment follows:

Clouds → Rain

The fancy, technical term for this idea is "the contrapositive." What we've done in the diagram above is negated the necessary condition, negated the sufficient condition, and reversed their order.

A much easier way to think about it though is just that we don't have the necessary condition. Clouds are the necessary condition because they're needed for rain. And if we don't have what we need for rain, then it follows that it won't rain.

Chaining Conditionals

We know that if it's rainy, then it's cloudy. What if I introduce another conditional relationship, can we make any inferences by combining the two? Consider this:

"If it's cloudy, I won't get a tan."

Try to translate this into conditional logic - what's sufficient, and what's necessary?

Clouds guarantee no tan. So the diagram would be:

Clouds → tan

Now we have a statement with clouds as a sufficient condition and our original statement from earlier in the lesson where clouds were the necessary condition. We can "chain" or "link" those statements together as follows:

Rain → Clouds
Clouds → Tan

Rain → Tan

This makes sense, right? If it's rainy it's cloudy, and therefore I won't get tan. The contrapositive also follows, if I do get tan then it must not be cloudy and also must not be rainy:

Tan → Rain

Flaw 1: Sufficient/Necessary Swaps

One of the most common flaws on the LSAT is when the test writers improperly use conditional logic. Frequently they will take the necessary to guarantee the sufficient, which I call a sufficient/necessary swap.

Using the same example of if it's rainy, then it's cloudy, the LSAT may improperly infer that if it's cloudy then it must be raining. LSAT students who understand conditional logic know that this is not the case! The necessary condition doesn't guarantee anything. So if it's cloudy it might be raining, but it might not be raining.

Here's another example:

If you love sailing, then you spend much of your time on lakes or oceans. Smitty spends much of his time on lakes and oceans, so he must love sailing.

This argument is flawed because it takes the necessary condition (spending time on lakes or oceans) to guarantee the sufficient (loving sailing). Smitty may spend time on the water because he loves motorboats, or waterskiing, or surfing, not necessarily sailing.

The argument swapped the sufficient and necessary conditions! This is illogical.

The diagram of this flawed argument would look like this:

E: Love sailing → Spend time on lakes or oceans
C: Spend time on lakes or oceans → Love sailing

Flaw 2: Improper Negation

The other common way that the test will incorrectly use conditional logic is by negating the sufficient condition and then claiming that the necessary definitely won't follow. This is incorrect because the sufficient condition is not needed for the necessary.

To use the Rain → Clouds example, the test may incorrectly claim that if it's not rainy then it's not cloudy. This is not true! Rain is unnecessary for clouds, so if it's not raining it could be cloudy or not cloudy. We don't know.

Here's another example:

In order to place top 10 in the marathon, Veronica needed to train hard. Veronica came in 67th place, so she must not have trained hard.

This is illogical! It negated the sufficient condition, and then claimed that the necessary condition must not have happened. But there are plenty of reasons why Veronica may not have finished top 10 besides a lack of training. Maybe she had a nagging injury and couldn't hit her best time, maybe the other runners were all extremely strong Olympians, maybe she actually trained so hard that she was tired on race day.

You can't just negate both sides of a conditional relationship. That's not a logical inference.

Here's the diagram of this flawed argument:

E: Top 10 → Train hard
C: Top 10 → Train hard

Navigate to the Sufficient/Necessary Swap and Improper Negation sections in the Identify the Flaw lesson for more practice!