• Contact Us
  • Student Login
  • My Cart

LSAT and Law School Admissions Blog

You are here: Home / Conditional Reasoning / Negating Compound and Conditional Statements

September 17, 2016

Negating Compound and Conditional Statements

Negating Compound and Conditional Statements

The ability to logically negate a statement—whether conditional, causal, etc.—is critical to your success on the LSAT. It comes up most commonly in the Logical Reasoning section of the test, although any question stem using the word “EXCEPT” (always capitalized) will require you to logically negate that stem.

The list does not stop here. Every time you apply the contrapositive of a conditional statement, you will need to reverse and negate the two conditions that constitute that statement.

This is relevant to Must Be True, Justify, and Parallel Reasoning questions mostly, but can also be critical in other sections of the test. Negating statements is also useful in Assumption questions because proving the correct answer choice requires the application of the Assumption Negation Technique: the correct answer choice, when logically negated, must weaken the conclusion of the argument. And, of course, the ability to understand the logical opposite of a conditional statement will be directly relevant to many Cannot Be True questions, where the correct answer choice is the one that can be disproven using the information contained in the stimulus.

Negating a Statement

As described in The PowerScore Logical Reasoning Bible (and in Lesson 2 of our Full Length LSAT course), negating a statement consists of creating the logical opposite of that statement, i.e. a statement that denies the truth of the original. The logical opposite of Jon is wise is Jon is not wise. The affirmative and negative counterparts of the oppositional construct are mutually exhaustive as well as mutually exclusive.

The same is true of quantified expressions. For instance, the logical opposite of I gained more than 20 points on my latest practice test is I did not gain more than 20 points on my latest practice test. How many points did you actually gain? The only possibility precluded is the possibility of gaining more than 20 points. You could have gained exactly 20 points, or maybe you did not gain any. In quantity constructs, all/not all, some/none, most/not most are logically proper oppositional constructs. By contrast, a construct such as All pleasure is good/No pleasure is good does not contain a logical opposition, because these opposites do not mutually exhaust the domain.

Understand the Implications

Formulating logical opposites may seem mechanistic, and in many ways it is. Nevertheless, it is important to understand the implications of your oppositional construct. Take, for instance, the logical opposite of I believe that stealing is moral. The correct form of the logical opposite (I do not believe that stealing is moral) amounts to a negation of the embedded clause (I believe that stealing is not moral). Similarly, when logically negating a statement such as It is rational not to eat food that is poisonous, consider the implications of the double negative construct (It is not rational not to eat food that is poisonous) and immediately simplify it: It is rational to eat food that is poisonous.

Negative statements are generally less informative than affirmatives; they are more complex and harder to process. Simplification is key!

Conditional Statements

What happens when you need to negate a conditional statement? In that case, you need to show that the sufficient condition can occur even if the necessary condition does not occur, i.e. that the necessary condition is not, in fact, necessary. So, the logical opposite of “All that glitters is gold” is simply “All that glitters is not gold.” To put it another way, some things may glitter even if they are not gold, because not everything that glitters is gold.

Quite often, the logical opposite of a conditional statement is formed using the phrase “even if.” The logical opposite of the statement Unless you practice, you will not succeed is You can succeed even if you do not practice. This is because the original statement posits practicing as a necessary condition for success (Succeed –> Practice). To contradict this statement, you need to show that practice is not a necessary condition for success. Note that even if is not, by itself, an indicator of a sufficient condition: it merely states that the lack of practice does not prevent one from succeeding, not that the lack of practice somehow ensures success.

Compound Statements

Now, consider what happens when negating compound sentences, such as conjunctions of the form X and Y and disjunctions of the form X or Y (or both).

To negate a conjunction such as I love you and you love me requires showing that the two clauses cannot be both true: it is simply not the case that we both love each other. Using De Morgan’s laws for interrelating conjunctions and disjunctions, this would mean one of three things: either I don’t love you, or else you don’t love me, or else neither of us loves the other. The either/or construction does not preclude the possibility of both propositions being true, unless specifically told otherwise (e.g. either X or Y, but not both).

To negate a disjunction such as Jon is either a doctor or a lawyer requires showing that Jon is neither a doctor nor a lawyer (i.e. that Jon is not a doctor and that Jon is not a lawyer). At the most basic level, negating a conjunction (and) requires the use of or, whereas negating a disjunction (or) requires the use of and.

If you wish to practice sentential negation of propositions that are both conditional and compound, try these out:

  • Only those who are both romantic and cautious can truly fall in love.
  • You are not a realist unless you either believe in miracles or in yourself.
  • You are neither a realist nor a humanist if you believe in miracles.
  • It is rational not to believe in miracles, unless you are either romantic or idealistic.

If you’d like to run your answers by us, feel free to use the Submit Comment button below.

Good luck!

FacebookTweetPinEmail

Posted by PowerScore Test Prep / Conditional Reasoning, LSAT Prep / Conditional Reasoning, LSAT Prep Leave a Comment

  • arindom
    May 02, 2016 at 12:49am

    Could you please check my answers?

    1) Even if you fall in love, you are not a romantic or you are not cautious.

    2) Even if you are a realist, you do not believe in miracles and you do not believe in yourself.

    3) Even if you believe in miracles, you are either a realist or a humanist.

    4) Even if it is rational to believe in miracles, you are not a realist and not an idealist.

    Thanks.

    – Arindom

  • Nicolay Siclunov
    May 03, 2016 at 12:37pm

    Hi Arindom,

    Thanks for taking a stab at my quiz! However, your answers need to be tweaked a little. Take a look at the answer key:

     

    Only those who are both romantic and cautious can truly fall in love. (Fall in Love –> Romantic AND Cautious)

    Negates to: To fall in love, you don’t need to be both romantic and cautious. In other words, it is possible to fall in love even if you are not romantic or cautious. It may even be possible to fall in love if you are neither romantic nor cautious. The logical opposite of the statement would suggest that romance and caution are not necessary conditions for falling in love.

     

    You are not a realist unless you either believe in miracles or in yourself. (Realist –> Believe in miracles OR Believe in yourself)

    Negates to: You can be a realist even if you don’t believe in miracles AND you don’t believe in yourself. In other words, the sufficient condition can occur (being a realist) even if neither of the two necessary conditions were to occur.

     

    You are neither a realist nor a humanist if you believe in miracles. (Believe in miracles –> NOT Realist AND NOT Humanist)

    Negates to: It is possible to believe in miracles even if you are a realist or a humanist. It is also possible to believe in miracles if you are both.

     

    It is rational not to believe in miracles, unless you are either romantic or idealistic. (Rational to believe in miracles –> Romantic OR Idealistic)

    Negates to: It’s rational to believe in miracles even if you are neither romantic nor idealistic (i.e. NOT romantic AND NOT idealistic). In other words, you don’t have to be either romantic or idealistic in order to believe in miracles.

     

    Remember – when negating conditional statements, you need to show that the sufficient condition can occur even in the absence of the necessary condition.

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Attend a PowerScore Webinar!

Popular Posts

  • Podcast Episode 168: The 2025 US News Law School Rankings
  • Podcast Episode 167: April 2025 LSAT Recap
  • Podcast Episode 166: LSAT Faceoff: Dave and Jon Debate Five Common Test Concerns
  • Podcast Episode 165: February 2025 LSAT Recap
  • Podcast Episode 164: State of the LSAT Union: 2024 Recap and 2025 Preview

Categories

  • Pinterest
  • Facebook
  • YouTube
  • Twitter
Share this ArticleLike this article? Email it to a friend!

Email sent!