The Logical Opposite

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I hope your weekend went by splendidly and your LSAT prep is going well. I thought we could start off the week right with a great review of a very important concept: negation.

As you work through your LSAT questions you’ll find that once in a while you are tasked with negating certain LSAT sentences. Hopefully, you’ve noticed that negating a sentence on an LSAT question is somewhat different than negating a sentence in the real world. The key to negating is always asking yourself: what is the minimum required to disprove this statement.

So, starting with the basics: there are three types of statements that we can negate on the LSAT: Quantifier statements, Sufficient & Necessary statements, and—for lack of a better word—“Regular” statements.

Let’s begin with quantifiers.

As you know, all quantifiers fall under the 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 of the puppies in the litter are spotted.”

Logical opposite:

“None of the puppies in the litter are spotted.”

Now let’s discuss Sufficient & Necessary statements. Let’s look at the following example:

“All the Dalmatian puppies in this litter have spots."

We can read this: If it is a Dalmatian puppy from this litter, then it has spots.

Contrapositive: If it does not have spots, then it is not a Dalmatian puppy from this litter.

So, how do we negate the above sentence? We must show that the sufficient condition can exist without the existence of the necessary condition. An easy way to remember this idea is to consider the logical opposite of “all” to be “not all.” So, the logical opposite of our statement would be: “Not all the Dalmatian puppies from this litter have spots.”

And lastly, we shall cover “regular” statements. These statements consist of those that have no quantifiers and are not Sufficient & Necessary statements.

For example:

“The puppy is asleep.”

How do we negate this sentence?

“The puppy is not necessarily asleep.”

It’s important to point out that the negation is not “The puppy is awake.” Instead, we hold that the logical opposite of “being asleep” is “not being asleep,” i.e. the minimum required to disprove that the puppy is asleep. The puppy being drowsy, unconscious, or in-and-out of sleep could negate the original sentence.

Mastering negation on the LSAT is imperative. We’ll go over each category in depth in the upcoming weeks. But, in the meantime, get in your negation practice by negating the statements you encounter during your prep!

Happy Studying!

Updated on Aug 18, 2016