LSAT Advanced Formal Logic

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Formal Logic plays a crucial role in the Law School Admission Test (LSAT), as it is designed to test a candidate’s ability to analyze and draw logical conclusions. One common type of logical reasoning question on the LSAT involves conditional statements, expressed in the form of “if/then” statements. These statements establish a relationship between two variables, where the truth value of one variable is dependent on the other. For example, if we have the statement, “If it is raining, then the ground is wet,” we can infer that if it is indeed raining, we can conclude that the ground will be wet.

Advanced Formal Logic

Conditional statements are often tested on the LSAT by asking candidates to determine the validity of a conclusion based on a given set of conditional statements. Additionally, the LSAT can introduce words like “only,” “not/unless,” and “only if” to complicate the conditional statements further. For instance, consider the statement, “Only if I have studied, then I will pass the exam.” This statement suggests that studying is a necessary condition for passing the exam. Therefore, if someone did not pass the exam, we can conclude that they did not study.

Another example would be a statement involving the word “unless.” For instance, “I will go jogging unless it’s raining.” In this case, the person will go jogging as long as it is not raining. Therefore, if it is raining, the person will not go jogging.

These concepts can be tested on the LSAT to assess a candidate’s ability to understand the implications of conditional statements accurately. By incorporating modifiers like “only,” “not/unless,” and “only if,” the LSAT challenges test-takers to carefully consider the conditions and their consequences. A strong understanding of formal logic and the ability to distinguish between necessary and sufficient conditions are fundamental skills required to excel on the LSAT. It is important for candidates to practice identifying logical connections and drawing valid conclusions based on conditional statements in order to achieve success on this test.

Formal Logic Practice Question


Craig will not take organic chemistry unless Paula lends him her notes from when she took the class.

Which of the following is/are consistent with the statement above? [Choose all that apply]

(i) Paula does not lend her notes and Craig does not take organic chemistry.
(ii) Craig takes organic chemistry using only Linda’s notes.
(iii) Craig does not take organic chemistry even though Paula lends him her notes.
(iv) Craig receives a B+ in organic chemistry.

Correct Response: (i), (iii), and (iv) only.

Explanation


“Consistent” statements are statements that can both be true. (i) represents the contrapositive of the original statement, so not only is (i) consistent with the original statement, it follows from it.

In (iii), Paula has provided the necessary condition for Craig’s taking Orgo – that is, she lends her notes – but necessity is not the same thing as sufficiency. It’s therefore quite consistent with the statement that, even with Paula’s notes in hand, Craig elects not to take Orgo. (This is a very important concept.)

As for (iv), Craig’s grade is outside the scope of the statement, so it’s quite consistent that he get a B+. “Consistent” doesn’t mean “inferable” or “logically equivalent,” and now you know that even if you didn’t before!
(ii) is the only Impossible statement, since Paula’s notes are a necessary condition for Craig’s taking Orgo. For him to take the course without Paula’s notes would be inconsistent with the statement.

Additional Practice:

Only If

Statement: “I will go to the party only if my best friend goes too.”

Under what condition will the student go to the party?

(A) Only if the student’s best friend does not go
(B) Only if the student’s best friend goes
(C) The student can go to the party regardless of whether their best friend goes or not
(D) The student cannot go to the party even if their best friend goes

Correct answer: (B) Only if the student’s best friend goes

Explanation: The statement indicates that the student will only go to the party if their best friend also goes.

No/Unless

Statement: “I will not eat dessert unless it is chocolate.”

Which type of desserts will the student eat?

(A) Only chocolate desserts
(B) Only non-chocolate desserts
(C) Both chocolate and non-chocolate desserts
(D) The student will not eat any desserts

Correct answer: (A) Only chocolate desserts

Explanation: The statement states that the student will not eat dessert unless it is chocolate, implying that they will eat chocolate desserts.

Only with
Statement: “I will watch the movie only with my sister.”

With whom will the student watch the movie?

(A) Only with their sister
(B) Only without their sister
(C) The student can watch the movie with or without their sister
(D) The student cannot watch the movie regardless of whether their sister is present or not

Correct answer: (A) Only with their sister

Explanation: The statement indicates that the student will only watch the movie if their sister is present.

No/Unless
Statement: “I will not travel to Europe unless I save enough money.”

Under what condition will the student travel to Europe?

(A) The student will travel to Europe regardless of saving enough money
(B) The student will travel to Europe only if they do not save enough money
(C) The student will travel to Europe only if they save enough money
(D) The student cannot travel to Europe even if they save enough money

Correct answer: (C) The student will travel to Europe only if they save enough money

Explanation: The statement implies that the student will not travel to Europe unless they save enough money, indicating that they will only travel if they have enough savings.

Previous: Formal Logic: Necessary vs. Sufficient
Next: What’s Tested on the LSAT: Logic Games

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