LSAT Logic and Negation Rules

Vocabulary and rule-based flashcards covering logical negations, quantifiers, and symbolic operations for LSAT preparation.

Negation of "Some A are B"

No A are B.

Negation of "Some A are not B"

All A are B.

Negation of "All A are B"

Some A are not B.

Negation of "Every A is B"

Some A is not B.

Negation of "No A are B"

Some A are B.

Negation of "None of A are B"

Some A are B.

Many (LSAT convention)

At least one ($1+$). Therefore its negation is none/zero.

Most / Majority

$>50\%$.

Negation of Most / Majority ($>50\%$)

$\le 50\%$. Not merely $<50\%$.

Minority

$<50\%$.

Negation of Minority ($<50\%$)

$\ge 50\%$.

Symbolic Negation of Existential E

$$\neg \exists x P(x) = \forall x \neg P(x)$$

Symbolic Negation of Universal A

$$\neg \forall x P(x) = \exists x \neg P(x)$$

Freeze Group Rule

What you should do with the subject/group when negating: FREEZE IT. Keep the same group; negate the claim made about that group.

Negation of "Every [A who is X] is B"

Some [A who is X] is not B. Do not change X.

"Didn't do any B"

Did zero B. Negation = did at least one B.

Negation of "No A did any B"

Some A did at least one B.

Negation of A or B

not A AND not B. $\neg(A \lor B) = \neg A \land \neg B$

Negation of A and B

not A OR not B. $\neg(A \land B) = \neg A \lor \neg B$

Negation of If $A \rightarrow B$

A AND not B. That's the only situation making the conditional false.

Handling "Unless A, B"

Translate to $\neg A \rightarrow B$. Negation = not A AND not B.

Biggest Mistake with Complicated LSAT Negations

Negating every quantifier in sight instead of identifying the outer logical structure.

Fast LSAT Negation Procedure

1. Outer quantifier → 2. Freeze group → 3. Flip quantifier → 4. Negate claim → 5. Simplify if necessary.

Proposed Negation Verification Test

Ask: Could the original and my version both be true? If yes, your version is not the negation.