Logical Reasoning and Problem Solving: Deduction and Assumptions
What the paper tests
Logical Reasoning and Problem Solving tests valid deduction, not general intelligence. Items include syllogisms, conditional statements, ordering puzzles, assumptions, strengthening and weakening, and conclusions drawn from short passages. The skill is to separate what must be true from what is merely plausible.
Core rules and concepts
- Valid conditional forms: modus ponens - if P then Q; P; therefore Q. Modus tollens - if P then Q; not Q; therefore not P.
- Invalid forms: affirming the consequent - if P then Q; Q; therefore P. Denying the antecedent - if P then Q; not P; therefore not Q.
- Quantifiers: all, some, no. 「Some A are B」 asserts at least one overlap; it does not by itself mean most A are B or that some A are not B.
- Necessary vs sufficient: 「only if」 introduces a necessary condition; 「if」 introduces a sufficient condition.
- Ordering puzzles: draw a line or table and place fixed items first; propagate constraints.
- Assumption questions: the answer must be required by the argument, not merely helpful or true.
Worked example
Premises: 「If an officer is authorised to conduct the operation, the officer has completed the specialist course. Officer A has not completed the specialist course.」 Conclusion: 「Officer A is not authorised to conduct the operation.」 This is valid modus tollens. Let P = authorised, Q = completed. The premises are P → Q and not Q; therefore not P. By contrast, 「Officer B completed the course, so Officer B is authorised」 is invalid: it affirms the consequent.
Traps
- Reversing a conditional and treating the converse as equivalent.
- Reading some as most or as some but not all.
- Adding an unstated assumption that makes the argument work.
- In strengthening/weakening items, choosing an answer that is relevant but does not affect the conclusion.
- Solving an ordering puzzle from memory instead of writing down the constraints.