Logical Deduction
Logical Deduction
Logical Deduction tests whether you can draw conclusions that must follow from given premises, even if the premises are false in reality. You may see syllogisms, conditional statements, or ordering puzzles.
Core rules
- Validity is about form, not truth. "All A are B; all B are C; therefore all A are C" is valid regardless of what A, B, and C stand for.
- Conditional: "If P then Q" does not imply "if Q then P". It does imply "if not Q then not P" (contrapositive).
- Quantifiers: "All" distributes; "some" is symmetric ("some A are B" means "some B are A"); "no" is symmetric.
- For ordering puzzles, list fixed positions and eliminate possibilities step by step.
- Only accept a conclusion if every premise-compatible scenario makes it true.
Worked example
Premises: "All teachers are graduates. Some graduates are cyclists." Which conclusion must be true? (a) Some teachers are cyclists. (b) Some cyclists are graduates. (c) All cyclists are graduates. (a) does not follow: the cyclists who are graduates may not be teachers. (b) follows directly from "some graduates are cyclists" by symmetry. (c) is too strong. Answer: (b).
Traps
- Affirming the consequent: from "if P then Q" and "Q", concluding "P".
- Converting "all A are B" into "all B are A".
- Treating "some" as "some but not all" when it only means at least one.
- Adding real-world knowledge to fill gaps.
- Accepting a conclusion that is merely possible, not necessary.