Overview
This lecture covers conditional reasoning for the LSAT, including how to recognize, diagram, and infer from conditional statements, as well as common mistakes and complex statement forms.
Basics of Conditional Statements
- Conditional statements have a sufficient condition (if true, guarantees outcome) and a necessary condition (must be true if the sufficient is true).
- Example: "All cats have tails" means if something is a cat (sufficient), it must have a tail (necessary).
- Diagram: C → T (if Cat, then Tail).
Inferences and Contrapositives
- The contrapositive swaps and negates the original conditions: ~T → ~C ("If not Tail, then not Cat").
- Only the necessary condition can be proven by the sufficient, not vice versa.
- Incorrect reversal: T → C ("If Tail, then Cat") is wrong.
- Incorrect negation: ~C → ~T ("If not Cat, then not Tail") is wrong.
Importance of Diagramming
- Diagrams help quickly visualize and recall relationships.
- Diagrams make it easier to see inferences and avoid language confusion.
LSAT vs Real Life
- LSAT conditionals are assumed absolutely true, regardless of real-world exceptions.
- Take LSAT statements at face value without considering possible exceptions.
Complex Conditional Statements
And Statements
- Example: "If it is hot and Brian is outside, he will be sweaty" → H and O → S.
- Contrapositive: ~S → ~H or ~O.
- Both sufficient conditions must be true for the necessary result.
Or Statements
- Example: "If Talissa has a son, she will name him John or Dan" → S → J or D.
- Contrapositive: ~J and ~D → ~S.
- For or in sufficient: C or R → ~W (Candy or Rocks → Not Well), contrapositive: W → ~C and ~R.
If and Only If Statements
- Means both conditions guarantee each other.
- Example: O ↔ S (Watching Office if and only if with sister); both O → S and S → O.
- Both contrapositive forms apply.
Conditional Statements on the LSAT
- Conditional reasoning appears frequently in Logic Games and Logical Reasoning.
- Key in question types: Parallel Reasoning, Sufficient Assumption, Must Be True, Principle, Flaws.
- Mistakes in questions often involve incorrect reversals or negations.
Key Terms & Definitions
- Conditional statement — a statement with a sufficient and necessary condition (If X, then Y).
- Sufficient condition — triggers the necessary condition if true.
- Necessary condition — must be true if the sufficient condition is true.
- Contrapositive — both swaps and negates the conditions of a conditional statement.
- Incorrect reversal — reverses the conditions without negation; not a valid inference.
- Incorrect negation — negates without reversing conditions; not a valid inference.
Action Items / Next Steps
- Practice diagramming conditional statements and their contrapositives.
- Review negations and practice identifying incorrect inferences.
- Read the linked article on negations for deeper understanding.