People who are red/green color-blind cannot distinguish between green and brown. Gerald cannot distinguish between gr...

AndreaK March 29, 2020

Hi @nicolebet,

Glad to hear you are getting the hang of diagramming! This is a really important skill for understanding the LSAT. Note I say it’s an important skill for understanding the LSAT—not necessarily so for taking the official test!

Diagramming helps us see flaws (such as mistaken reversals and mistaken negations) sometimes more clearly. It also helps us fill in missing premises, strengthen arguments, and the like! However, I personally see diagramming as more of a learning tool. It helps you learn conditional logic inside and out. When you get good at conditional logic, you may find that you no longer need diagramming.

When I started studying for the LSAT, I HATED diagramming. It was hard for me to interpret. It thought it was messy, unintuitive, and far too easy to make mistakes with.

Honestly, I still feel that way about diagramming. That’s why I try to teach my students to pick up on the more intuitive understanding of logic. I also think that’s faster.

That being said, we all start at different baselines. When my intuition failed me, I would pause and try to diagram a confusing stimulus. That was often slow and grueling. However, it really helped me strengthen my skills recognizing conditional logic. Though you don’t always need to write it out (diagramming), you do need to be able to follow the deductions and understand their underlying meaning. Though it can sometimes feel like a counterintuitive approach, diagramming can help strengthen this skillset.

That was a long answer to your last question, but here’s my key takeaway. If you can recognize the answer without diagramming, save time and don’t diagram! It’s never true that you NEED to diagram on the LSAT. Diagramming is just a tool that can help people in their efforts to better understand conditional logic. If you are stuck between two answer choices that both seem like they might be right, maybe diagramming is a good fallback safety measure. Or, finding the flaw in the incorrect answer choice using deductive reasoning may work better for you. Everyone is different! I would say use diagramming when you don’t understand a question or answer choice. That will help you strengthen your skillset in itself. I don’t think it’s an efficient use of your time to diagram questions you understand well, however!

Now on to your discussion about the contrapositive.

If you become stuck after diagramming, maybe that’s partially because of the reasons I mentioned above regarding why I personally had trouble with it. Seeing a bunch of characters and slashes and arrows...that’s unintuitive to what you’re reading! If that confuses you, remember diagramming simply is representing an abstract idea symbolically. If you don’t need the symbols to understand the idea (or worse, the symbols make the ideas more confusing) then maybe try to focus on understanding the underlying ideas at play and how they interact with one another. I do think it’s important to know how to diagram for when you need it, but I don’t think it’s helpful to diagram a problem if that’s only going to make it more confusing than understanding the ideas as words with meaning would be.

Let’s use this question as our example.

People who are red/green color blind cannot distinguish between green and brown.

If you are red/green color blind —> CANNOT distinguish between green and brown

Contrapositive: if you CAN distinguish between green and brown —> then we know for sure you are NOT red/green color blind.

That’s logically valid.

The next part of our stimulus says:
Gerald CANNOT distinguish between green and brown —> therefore Gerald is red/green color blind

Now hold up just a minute. From a diagramming standpoint (our symbolic representation of ideas here), we can see that’s an INVALID reversal of the first statement in the stimulus. For the contrapositive (which is VALID), you have to BOTH reverse and negate, and here it is only reversing. This is known as the fallacy of the converse or mistaken reversal.

Now, why is that a fallacy? From an intuitive standpoint, why is that mistaken reversal not saying the same thing as the original statement (or its contrapositive, which is another way of thinking of the original statement) is?

The original statement just says that if a person is R/G color blind, they MUST not be able to distinguish between green and brown. But if a person can’t distinguish between green and brown (maybe they can’t distinguish because they’re blindfolded or in a dark room) it isn’t necessarily true that they MUST be color blind. The reversal unjustifiably rules out possible scenarios, like the ones mentioned.

Our contrapositive says that if Gerald CAN distinguish between green and brown, then we know he is not red/green colorblind. That’s just another way of understanding the original statement that if a person is R/G color blind, they must not be able to distinguish between green and brown.

The contrapositive is tested often on questions with conditional logic, like must be true questions. The contrapositive is a valid statement. However, reversing without negating, or negating without reversing changes the meaning of the ideas at play. It changes what the possible scenarios within a conditional rule are because it alters the restrictions of the original statement.

For parallel questions, you want to match the answer choice to the original structure of the stimulus. If the stimulus makes a flaw (like is the case here), you want the answer choice to then make the same flaw.

Let’s take a look at our correct answer.

If you suffer from sinusitis —> lose your sense of smell
Mary lost her sense of smell —> suffers from sinusitis

As with what takes place in our stimulus, the second portion is a mistaken reversal. Mary could have lost her sense of smell for other reasons (old age, an infection, medical condition, wearing too much strong perfume too often, ect.). It’s not necessary that she lost it only because of sinusitis.

Hope this helps! Feel free to follow up if you have anymore questions!

nicolebet March 29, 2020

Hello Andrea,
It did help, I just still am not understanding what is meant when it is said that the 'contrapositive is being tested.' Can we go through an example of this?
What is revealed with contrapositive diagrammed?

nicolebet April 13, 2020

Hello Andrea,
It did help, I just still am not understanding what is meant when it is said that the 'contrapositive is being tested.' Can we go through an example of this?
What is revealed with contrapositive diagrammed?

shunhe May 2, 2020

Hi @nicolebet,

Let me see if I can help explain the contrapositive, which is a pretty important concept we'll need on the test.

First, let me just tell you what it is. Let's say we have the conditional statement X-->Y. The contrapositive of this statement is going to be ~Y --> ~X.

The thing that's special about the contrapositive is that it's always going to be true when the original statement is true. So if we know X --> Y, then we know ~Y --> ~X.

Now, this is all a bit abstract, so let's take a look at a concrete example. Let's say that if I go to Chipotle, I will get burrito with guac.

Now what do we know? Let's say I do go to Chipotle. Then we also know that I must've gotten a burrito with guac.

But let's say that I didn't get a burrito with guac. Then what do we know? That I can't have gone to Chipotle! Why? Because if I had gone to Chipotle, I would've gotten a burrito with guac. But I didn't. So I couldn't have gone to Chipotle. And this is just applying the contrapositive!

So sometimes we'll have a passage where we might have
A --> B
~C --> ~B

And if we take the contrapositive of the second statement, we'll get B --> C, which we can then link with the first statement to get

A --> B --> C

And this is the kind of thing that diagramming the contrapositive can reveal.

Hope this helps! Feel free to ask any other questions that you might have.