Logic, Reasoning, and Problem Solving
What this domain tests
Logic, Reasoning, and Problem Solving tests deductive validity, conditional statements, quantifiers, sequencing, assumptions, and cause-and-effect. You must separate what must be true from what could be true.
Core rules
- In a conditional, If P then Q, P is sufficient for Q; Q is necessary for P. The converse, If Q then P, is not automatically valid.
- 'Only if' introduces a necessary condition: P only if Q means If P then Q.
- 'All' and 'no' support strong inferences; 'some' does not support 'all'.
- A valid conclusion follows from the premises even if the premises are false in the real world.
- Correlation does not prove causation; alternative explanations must be considered.
Worked example
Premise: If a vehicle is reported stolen, it is flagged in the database. Premise: This vehicle is flagged in the database. Conclusion: Therefore, this vehicle is reported stolen. Reasoning: The argument has the form If P then Q; Q; therefore P. That is affirming the consequent and is invalid. The vehicle could be flagged for a stolen plate, an investigative hold, or a data error. A valid conclusion would be: If this vehicle is reported stolen, then it is flagged; this vehicle is reported stolen; therefore it is flagged.
Traps that cost marks
- Reversing a conditional and treating the converse as certain.
- Reading 'some' as 'all' or 'most'.
- Adding an unstated assumption as if it were a premise.
- Confusing sequence with causation.
- Rejecting a valid argument because you dislike its content.