Formal logic notation, quantifiers, and valid inference rules used in LSAT logical reasoning and logic games. Front: the term or rule. Back: a plain-language definition or example.
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- What does 'All S are P' mean?
- Every member of set S is also a member of set P. A universal affirmative statement.
- What does 'No S are P' mean?
- No member of set S is a member of set P. A universal negative statement.
- What does 'Some S are P' mean?
- At least one member of set S is also a member of set P. A particular affirmative statement.
- What does 'Some S are not P' mean?
- At least one member of set S is not a member of set P. A particular negative statement.
- What is a sufficient condition?
- A condition whose presence guarantees the conclusion. If A is sufficient for B, then A being true means B must be true.
- What is a necessary condition?
- A condition that must be true for a conclusion to be true. If B is necessary for A, then A cannot be true without B.
- In 'If P then Q,' what is the relationship?
- P is the antecedent (condition). Q is the consequent (conclusion). If P is true, Q must be true.
- What is the contrapositive of 'If P then Q'?
- If not Q, then not P. The contrapositive is logically equivalent to the original statement.
- What is the converse of 'If P then Q'?
- If Q then P. The converse is NOT logically equivalent to the original.
- What is the inverse of 'If P then Q'?
- If not P, then not Q. The inverse is NOT logically equivalent to the original.
- What is Modus Ponens?
- If P then Q. P is true. Therefore, Q is true. A valid inference rule.
- What is Modus Tollens?
- If P then Q. Q is false. Therefore, P is false. A valid inference rule.
- What is the fallacy of Affirming the Consequent?
- If P then Q. Q is true. Concluding P is true. This is INVALID; Q could result from something other than P.
- What is the fallacy of Denying the Antecedent?
- If P then Q. P is false. Concluding Q is false. This is INVALID; Q could still be true for another reason.
- What is Hypothetical Syllogism?
- If P then Q. If Q then R. Therefore, if P then R. A valid inference rule.