If you diagram, you should look for deductions
- Sep 28, 2017
- Reviewed by: Matt Riley
We’ve spilled a lot of ink on this blog about how to diagram conditional statements, but you may be wondering why you should even bother acquiring this skill — what good is being able to diagram, anyway??
The answer, of course, is that it helps you understand what conclusions can validly be drawn from a set of information. Today we’ll discuss the types of valid inferences that can be made from conditional statements — and stay tuned next week, when we’ll circle back to talk about what LSAT question types most often require diagramming.
Valid Inference #1: Valid Affirmation
This one’s quite simple. Let’s say you know that all LSAT instructors are good looking.
LSAT → Good Looking
Let’s say you also know that my friend Bob is an LSAT instructor. From this information, you can conclude that Bob is good looking. To put it more generally, if you know that A always entails B, and you know that you have A, you can conclude that you also have B.
A → B
Valid Inference #2: Contrapositive
The contrapositive is the single most important thing to know about conditional statements. Take the example that “anyone with a fantasy football team has no life.”
Fantasy Football Team → No Life
Of course, knowing that someone does not have a fantasy football team doesn’t tell us whether that person has a life (that would be the inverse), and knowing that Rick has no life doesn’t necessarily mean he has a fantasy football team (that’s our pal the fallacy of the converse). However, we can conclude that if you have a life, you must NOT have a fantasy football team.
Life → No Fantasy Football Team
In other words, if you know that A → B, you can also conclude that NOT B → NOT A.
Valid Inference #3: Transitive Deduction
Here’s where things start getting crazy. Let’s say you know two pieces of information: Susie dances on the bar whenever she drinks tequila, and every Tuesday, Susie drinks tequila. If we pay attention to key words, we end up with a diagram that looks like this:
Tuesday → Drink Tequila
Drink Tequila → Dances on Bar
Every single Tuesday, Susie drinks tequila, and every single time she drinks tequila, she ends up getting all Coyote Ugly on her friends. We can conclude from these two statements:
Tuesday → Dances on Bar
Or, to state it in plain English, every Tuesday, Susie dances on the bar.
You can combine a limitless number of conditional statements transitively, as long as the necessary condition of a certain statement is the same as the sufficient condition of another. For instance:
Watch Game of Thrones → Stay up Late
Stay up Late → Sleep at Work
Sleep at Work → Boss Yells at Me
Every time I watch GOT, I end up staying up way too late. When that happens, I fall asleep at my desk. And when that happens, my boss yells at me. From these facts, we can draw the conclusion that:
Watch Game of Thrones → Boss Yells at Me
Put simply, when you know:
A → B
B → C
You can conclude:
A → C
Of course, diagramming isn’t always this simple – usually the hardest part is figuring out how to diagram a more complicated statement (which is why we belabor being able to identify diagramming key words!). But diagramming is essential when it comes to differentiating between supported and unsupported conclusions. Next week we’ll talk about the circumstances in which you’ll most often need this skill on the LSAT, so stay tuned!
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