Deductive Reasoning
What this section tests
Deductive questions give you premises and ask what must follow. Validity is about form, not about whether the statements are true in the real world. If the premises are taken as given, the conclusion either follows necessarily or it does not.
Concepts to master
- Conditional statements. If P, then Q. P is sufficient for Q; Q is necessary for P. The valid move is the contrapositive: If not Q, then not P.
- Quantifiers. All, no, some, none. "Some" means at least one, and it does not imply "some are not."
- Syllogisms. Chain the terms: All K-9 units are certified; all certified units are reviewed; therefore all K-9 units are reviewed.
- Validity vs. truth. A conclusion can follow perfectly from false premises; that is still a valid deduction.
Traps
Two invalid forms appear constantly:
- Affirming the consequent: If P then Q; Q; therefore P. Invalid.
- Denying the antecedent: If P then Q; not P; therefore not Q. Invalid.
Also watch illicit conversion (turning "all A are B" into "all B are A") and conclusions that merely restate a premise in different words - these are safe but sometimes not what was asked.
Rule of thumb
Write the conditional, then flip and negate: If P → Q becomes If not Q → not P. If the answer choice matches the flip-and-negate, it is valid. If it keeps the same order or negates only the first half, it is a trap.
Worked example
All K-9 units are certified. Some certified units are trained in narcotics detection. Can we conclude that some K-9 units are trained in narcotics detection? No. The certified units that are narcotics-trained may be a different subset entirely. Overlap is possible, not guaranteed.