What is Conditional Reasoning?

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Conditional reasoning is reasoning involving conditional statements, an important skill to master for the LSAT. A conditional statement is not the same as a fact. A fact is absolutely true, where a conditional statement only tells you of a scenario in which something is true. It is important to be able to make inferences from conditional statements, as well as know what you can’t infer.

Anatomy of a Conditional Statement: Sufficient Conditions and Necessary Conditions

A basic conditional statement will have a sufficient condition and a necessary condition. If the sufficient condition is true, the necessary condition follows. In other words, there is a condition which is sufficient to necessarily cause a certain outcome.

My go-to example of a conditional statement is “All cats have tails”, which can be rephrased as “if something is a cat, it has a tail”. Being a cat is the sufficient condition, and having a tail is the necessary condition. Being a cat is sufficient to necessarily have a tail.

It is very useful to diagram conditional statements, and I would diagram our example like so:

C → T

Here, the arrow means that if the left side is true, the right side will also be true.

Remember, there are many ways conditional statements can be phrased, and the LSAT will rarely make it easy. Here are a few forms this statement could take:

“All cats have tails.”

“If something is a cat, it has a tail.”

“Something has a tail if it is a cat.”

“There is no such thing as a tail-less cat.”

“Any cat you can find will have a tail.”

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​What Can We Infer from a Conditional Statement?

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From our statement above, we know that all cats have tails. But that’s not all! Because we know that all cats have tails, we also know that if something does not have a tail, it is not a cat.

T → C

This is called the contrapositive of our original statement. Now, not having a tail is sufficient for something to necessarily not be a cat. You can find a contrapositive by swapping the sufficient and necessary conditions and then negating them both. (You can brush up on negations in my Negations article, if needed).

It is also important to know what you can’t infer from a conditional statement. When finding the contrapositive, you have to make sure you swap the conditions AND negate both. If we only swapped our conditions, we would end up with this:

T → C

This would tell us that if something has a tail, it is a cat. But this is an incorrect inference, because we know there are other animals with tails – dogs, sharks, lemurs, and many other animals all have tails. This is called an incorrect reversal, because we only reversed the conditions and didn’t negate them.

If we negated both sides but didn’t swap the conditions, we would get this:

C → T

This statement would say that if something is not a cat, it does not have a tail. This is also incorrect – all the animals I listed above are not cats and have tails. This is called an incorrect negation, because we negated the conditions but failed to reverse them.

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Remember: We can always prove the necessary condition with the sufficient condition – if something is a cat, it necessarily has a tail. That’s for certain.

However, we can never prove the sufficient condition. There is no way to prove that something is a cat. We can prove that something is not a cat, by showing that it has no tail. But we have no way to prove that something is a cat.

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Why Diagram Conditional Statements?

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The best thing about diagrams are that they’re efficient. You can look at your diagram and remember the relationships between terms much more quickly and accurately compared to remembering or re-reading the English sentences. This becomes more true as statements become more complex, or as you deal with more and more statements.

Compare this diagram:

C → T

T → C

With this sentence:

“There is no such thing as a tail-less cat.”

Once you’ve made your diagram and know what C and T represent, you’ll be able to recall their relationship at a glance when necessary. Additionally, inferences are easily included in the diagram, but harder to remember from the written statement alone.

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​The LSAT Is Not Real Life

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When you first read my “All cats have tails” statement, you may have thought something like “Well, Graeme, not all cats have tails.” And you’d be right. In real life, there are some cats that don’t have tails. There are very few absolutely true conditional statements in real life – as the old saying goes, there is an exception to every rule.

But the LSAT is not real life. If the LSAT tells you “All cats have tails”, that really means that all cats have tails. You have to take conditionals at face value, and assume that what they’re conveying is 100% true. If the LSAT says “Ben always wears a jacket when it rains”, that means always. He never forgets it, or loses it, or lends it to a friend – when it’s raining, Ben has that jacket. Remember this when interpreting conditional statements.

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​More Complex Conditional Statements

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The above cat example is pretty simple – there is only one term on each side. Unfortunately, conditional statements you see on the LSAT won’t always be simple. There are a few different types of more complex conditional statements. I’ll explain them here and cover what you can infer from them.

“And” Statements

Here is an example of a conditional “and” statement:

“If it is hot and Brian is outside, he will be sweaty.”

There are now two sufficient conditions: warm temperature and being outside. Both of these conditions must be met before we can necessarily say that Brian is sweaty. If Brian is outside when it’s cold, or if he is inside when it’s hot, we can’t definitively say that he is or is not sweaty. We can diagram this like so:

H and O → S

When inferring from an “and” statement, you do the same as a basic conditional statement – you swap the sides and negate both. Here is the resulting contrapositive (remember that when negating an “and” statement, it becomes an “or” statement):

S → H or O

In plain language, this means:

“If Brian is not sweaty, it must be not hot or Brian must not be outside.”

Remember to avoid the classic logic mistakes. If Brian is sweaty, that doesn’t mean it is hot or that Brian is outside. He could be working out in a gym. Similarly, if it is not hot or if Brian is not outside, he could still be sweaty for the same reason. We can never prove that it is hot or that Brian is outside.

You can also have an “and” with the necessary conditions:

“If Susan is feeling unwell, she will call in sick to work and stay home.”

Here, Susan feeling unwell is sufficient to necessarily say that she will call in sick and stay home. She will not call in sick to work and leave her house, nor will she stay home and work. We know that both must be true if she is feeling unwell. This statement can be diagrammed like this (where U is feeling unwell, C is calling in sick and H is staying home):

U → C and H

Making inferences is the same – swap and negate both sides, then change the “and” to an “or”.

C or H → U

In plain language, this means:

“If Susan doesn’t call in sick, or if she doesn’t stay home, she is not feeling unwell.”

Again, remember not to make mistakes here. All we know is what she does when she is unwell. If she doesn’t do those things, we know she isn’t unwell. Even if she stays home and calls in sick, we don’t know for certain that she is unwell.

“Or” Statements

Here is an example of a conditional “or” statement:

“If Talissa has a son, she will name him John or Dan.”

Here, there are two different necessary conditions – the son may be named John or Dan. While neither of them is necessary on their own, it is necessary that one of them occur if Talissa has a son. This statement can be diagrammed like so:

S → J or D

What can we infer from this statement? We negate “or” statements similarly to “and” statements – swap the conditions and negate all the terms, including changing the “or” to an “and”. Doing so here results in this:

J and D → S

In plain language, this means:

“If Talissa doesn’t name a child John and doesn’t name a child Dan, she didn’t have a son.”

It would be a mistake to say that if Talissa doesn’t have a son, she doesn’t name a child John or Dan. She could name a daughter John and still be in accordance with the original statement.

There can also be an “or” in the sufficient condition side. Consider the following:

“If I eat candy or rocks for breakfast, I won’t feel well.”

Either eating candy or eating rocks is sufficient to ensure that I do not feel well. I don’t need to eat both candy and rocks to not feel well – just one will do. This example can be diagrammed like so:

C or R → W

Note that this statement already has a negation – might be a bit of a curveball but nothing we can’t handle. Taking the contrapositive works the same as our Susan example, but remember that negating the negated term returns it to normal. We end up with this:

W → C and R

Translated to plain language, this means:

“If I am feeling well, I didn’t eat candy for breakfast and I didn’t eat rocks for breakfast.”

Again, make sure you properly make your inference. If I’m feeling unwell, it doesn’t mean I had rocks or candy for breakfast. And if I didn’t have rocks or candy for breakfast, it doesn’t mean I am feeling well.

It is also important to remember that these statements can be phrased differently. This statement in particular can even be phrased with an “or”:

“If I feel well, I didn’t have candy or rocks for breakfast.”

In reality though, because eating candy and eating rocks are separate terms, you should diagram this with “and” because we know C and R are both necessarily true.

“If and Only If” Statements

The third complex conditional statement is an “if and only if” statement. These are essentially two different conditional statements rolled into one – the “if” and the “only if”.

Consider the following example of a normal “if” statement:

“If I’m watching The Office, I’m with my sister.”

We can easily diagram and negate this:

O → S

S → O

Consider the following example of an “only if” statement:

“Only if I’m watching The Office am I with my sister.”

This is different from the first statement – it’s essentially saying “I’m only with my sister if we are watching The Office”, or “If I’m with my sister, we are watching The Office.” We can diagram and negate this too:

S → O

O → S

Now, consider the following “if and only if” statement:

“If and only if I’m watching The Office, I’m with my sister.”

This statement is a combination of both the above statements. As such, we can combine what we know about them:

O → S

S → O

S → O

O → S

As you can see, we can learn a lot from “if and only if” statements! You just have to remember to break them up into their two parts.

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Where Will I See Conditional Statements on the LSAT?

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Conditional statements are everywhere on the LSAT. They are very common in Logic Games sections, and you will need to master the ability to make quick inferences in order to push your score higher. Knowing how and when to make inferences allows you to better identify right answers, as well as identify which answers are incorrect.

For example, you might see a rule like:

“If Alyssa attends writing class on Tuesday, Jackson will attend writing on Thursday.”

Based on your knowledge of conditional statements, you know how to apply this rule to the facts. You should also be able to make an inference here – try it!

Conditional statements are also very common in Logical Reasoning sections. Any stimulus could contain conditional statements, but they are most commonly found in Parallel Reasoning, Flawed Parallel Reasoning, Sufficient Assumption, Must be True, and Principle question types. They are also common in some flaw questions – the flawed argument will often do an incorrect reversal or an incorrect negation. In any question, wrong answer choices can try to trick you with appealing incorrect inferences – so knowing what you can’t infer is equally vital.

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Further Reading

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​Negations on the LSAT​

How to Go Faster at LSAT Logical Reasoning

​When to Diagram LSAT Logical Reasoning Questions [Video]​

How to Draw LSAT Logical Reasoning Diagrams [Video]

​Facts vs Conditionals on the LSAT [Video]​

​Contrapositives [Video]​

​Get the LSATHacks LSAT Course​

​Get the Logical Reasoning Mastery Seminar​

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