Logical reasoning
Logical reasoning tests whether you can separate valid inference from plausible assertion. Expect conditional reasoning, syllogisms, ordering/grouping puzzles, argument assumptions, strengthen/weaken items, and short deductive games. Prior subject knowledge is unnecessary; formal structure is decisive.
Core rules and concepts
- Conditional “If P, then Q” licenses only the contrapositive “If not Q, then not P”. The converse “If Q, then P” and inverse “If not P, then not Q” are invalid.
- Distinguish sufficient from necessary: “P is sufficient for Q” means P→Q; “P is necessary for Q” means Q→P. “Only if” introduces a necessary condition.
- In syllogisms, “all”, “some”, and “no” have fixed scope. “Some A are B” guarantees at least one overlap but does not imply “all A are B” or “some A are not B”.
- For assumption questions, negate the candidate: if the argument collapses, the statement is necessary. For strengthen/weaken, target the evidence–conclusion link, not a side issue.
- In sequencing puzzles, draw slots and place fixed items first; propagate constraints and test the most restrictive rule.
Worked example
Premise: If a candidate scores above 700, she is invited to interview. Premise: Marta was not invited. Conclusion: Marta did not score above 700. This is valid: the contrapositive of P→Q is ¬Q→¬P. It would be invalid to conclude “Marta scored above 700” from an invitation, or “Marta was not invited” from a score at or below 700.
Traps that cost marks
Beware affirming the consequent, denying the antecedent, reversing “only if”, treating correlation as causation, and overreading “some”. In puzzles, do not assume an unstated ordering; every deduction must follow from a listed constraint.
Key points
- Valid conditional inference runs from ¬Q to ¬P, not from Q to P.
- “Only if” marks a necessary condition, not a sufficient one.
- “Some” means at least one, not all or most.
- Negate assumptions to test whether they are required.
- In puzzles, place fixed items before testing optional ones.