Source: https://www.manhattanprep.com/lsat/blog/logical-reasoning-negation-test/
Timestamp: 2019-04-21 22:58:16+00:00

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If you’ve been studying for the LSAT, you probably know that one Logical Reasoning question type (Necessary Assumption) involves something called the negation test. If you’re not aware of this, I recommend you stop reading this and search out information on that question type first!
In my classes and with my tutoring students, people usually accept the concept of the negation test. The concept isn’t the problem: how to correctly apply the concept is the sticking point.
I quickly realized that the negation test is more complicated than one chief weapon used to negate an answer choice.
So I came up with another.
I quickly realized that the negation test is more complicated than two chief weapons used to negate an answer choice.
And for quite some time, I struggled with where to draw a line. How many techniques does one need???
I eventually landed on three, keeping in mind that these are three specific applications of a very broad concept—you negate a choice by doing just enough to pop a balloon. You prick it with a pin. You don’t need dynamite, nor do you need to stomp on the balloon. You just need a pin-prick.
So let’s start with that concept.
Answer choice negation is all about reasonable doubt, if you’ll allow that analogy. In the U.S., when someone is on trial for some criminal act, the popular phrase is guilt “beyond a reasonable doubt.” In other words, the defense does not have to prove that the person charged with a crime is innocent; they merely need to provide reasonable doubt—maybe that person did not commit that crime.
Conditional statements are, in my process, categorized by two characteristics: they are absolute, and they are paired. Absolute in that the sufficient characteristic absolutely guarantees the existence of the necessary statement, and paired in that there are always two elements.
So how do you negate this? You remove the absolute nature, and you remove the pairing—give one of the elements without the other.
If you’re watching Netflix, you pay for internet access.
Diagramming this conditional statement may look something like N → IA. So how do we negate this?
The wrong way would be to take the incorrect negation…. ~N → ~IA. But this is not a negation—this is a completely unrelated statement. And notice this is still “absolute” and still “paired,” only this time the pairing is negative. Where once we had both items, N and IA, now both items are missing.
Even if you’re watching Netflix, you might not pay for internet access.
Notice I’ve switched to an “even if” phrasing, and I’ve introduced a “might.” That breaks the absolutist nature of the conditional. Then, I’ve kept one of the items (Netflix), but removed the other (pay for internet access).
This is something that takes practice, so I recommend you keep a simple template that makes sense to you—an “if X then Y” vs. “even if X maybe not Y” relationship—and put more complicated versions into a similar template.
The incorrect (but all too common) negation is to take the symbols as written and flip the negatives—the incorrect negation. ~C→D. But think about that for a moment. What this symbolic representation means is “everything not a cat is a dog.” So that toaster on the kitchen counter? Not a cat? Then it’s a dog.
I don’t think that’s the correct negation test wording.
When presented with an answer choice that relies heavily on quantifiers, words such as most, some, all, none, etc., I negate the quantity. You still have to apply logic, but I start with negating the quantity.
So what’s the opposite of all? Not all. What’s the opposite of some? None.
“All dogs are friendly” becomes “Not all dogs are friendly.” “Some palm trees grow on the beach” becomes “no palm trees grow on the beach.” You flip the logic of the quantity.
Those are negations that makes sense to me and help me understand the negation test concept. I just need to be careful when the original statement is negative—you’ll never be able to escape logical thought on the negation test. There is no “this one simple trick…” that will fit all cases.
“All dogs are not well trained.” So I would negate this as “not all dogs are not well trained”…but I don’t understand what that means. Double negations (not X are not Y) confuse me.
In answer choice negations, you need logical opposites. So absolute becomes non-absolute, or as I sometimes put it, rigid becomes relaxed.
Tom will go to the party v. Tom might not go to the party. Rigid v. Relaxed.
All oceans’ beaches have sand v. Not all beaches have sand. Rigid v. Relaxed.
Some people like the LSAT v. No people like the LSAT. Relaxed v. Rigid.
Whichever feeling is expressed in the original, make sure your negation has the opposite feeling.

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