LSAT Prep Concept: The Logical Opposite

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As you’ve hopefully fallen into a good LSAT prep groove, I thought we could go over a concept we haven’t covered in a long time: negating on the LSAT.

Once in a while during your LSAT prep, you will be tasked with negating a statement. Now, as with most things on the LSAT, negating statements is not as black and white as it is in the real world. What I want to refresh is how to find the “logical opposite” of a statement you encounter during your studies. The main question to ask yourself while negating a statement on the LSAT is: what is the minimum required to disprove this statement?

Now let’s start with the basics. There are three categories of statements that we negate on the LSAT: quantifiers, Sufficient & Necessary statements, and—for lack of a better word—“regular” statements. First, we’ll tackle quantifiers.

All quantifier sentences will fall under two categories: “some” and “most.” Any quantifier word that means “at least one” will fall under the “some” category. Likewise, any quantifier word that means “more than half” will fall under the “most” category.

So, the question is: what is the logical opposite of at least one? Well, what is the minimum required to disprove that you have at least one? You have none. Thus, the logical opposite of “some” is “none.”

Now, what is the logical opposite of more than half? Not more than half. "Not more than half" could be either “less than half” or “half.” So, the logical opposite of “most” is “50% or less.”

So, what is the logical opposite of the following sentence?

“Some apples on the tree have rotted.”

Logical opposite:

“None of the apples on the tree have rotted.”

Now let’s move on to Sufficient & Necessary statements.  Let’s begin with our favorite example:

“All berries are red.”

We can read this as: If it is a berry, then it is red.

Contrapositive: If it is not red, then it is not a berry.

Now, how would we negate this general principle? Did the image of a blueberry pop in your head? Good! The correct way to negate a general principle is to show that the sufficient condition can exist without the existence of the necessary condition. An easy way to remember this idea is to look at the logical opposite of “all” as “not all.” Thus, the logical opposite of our statement: “All berries are red,” becomes “Not all berries are red.” Thus, with the existence of just one single blueberry, we have negated the principle.

Lastly, let’s discuss “regular” statements. These are sentences that are not Sufficient & Necessary statements and do not have quantifiers.

For example:

“The tea is cold.”

How do we negate this sentence?

“The tea is not necessarily cold.”

It’s important to note that the negation is not “The tea is hot.” Instead, we hold that the logical opposite of “cold” is “not cold,” i.e. the minimum required to disprove that the tea is cold. The tea being lukewarm, warm, hot, or even scalding could negate the original sentence.

Properly negating sentences on the LSAT is a very important skill to master. I’ll make sure to post a few more blogs throughout these next few weeks so that you can continue practicing these techniques. But, in the meantime, you can get more negation practice by negating the statements you encounter during your prep!

Happy Studying!

Naz signature Updated on Aug 18, 2016