How to solve: Deductive Reasoning
What this category tests
Tests whether a conclusion necessarily follows from given premises — classic syllogisms, knights-and-knaves puzzles, and logic grids where you must isolate what's guaranteed true, not just plausible.
Where this typology comes from
Formal deduction goes back to Aristotle's theory of the syllogism around 350 BCE, and the "modus ponens / modus tollens" argument forms were codified soon after by the Stoic logician Chrysippus. The "knights and knaves" puzzle format — islands where every inhabitant always tells the truth or always lies — was popularized by mathematician and logician Raymond Smullyan in his 1978 book "What Is the Name of This Book?", building on earlier truth-teller puzzles.
How to approach it
Rewrite each premise in your own shorthand before combining them — don't try to hold the whole chain in your head. Build a grid or table when there are multiple entities and multiple attributes, and eliminate possibilities row by row. Judge every candidate conclusion strictly against what the premises guarantee, not what merely sounds consistent with them.
Worked example
On an island, every inhabitant is either a knight (always tells the truth) or a knave (always lies). You meet two islanders, Ana and Beto. Ana says: 'Beto is a knave.' Beto says: 'Ana and I are both knights.' What are Ana and Beto?
- Ana is a knight, Beto is a knave. ✓ Correct answer
- Ana is a knave, Beto is a knight.
- Both are knights.
- Both are knaves.
Explanation Check Beto's claim first, since it's a compound statement. If Beto were a knight, his claim 'Ana and I are both knights' would have to be true, making Ana a knight too — but then Ana's claim 'Beto is a knave' would also have to be true, which contradicts Beto being a knight. So Beto must be a knave. As a knave, his claim is false, which just means it's not true that both are knights — already satisfied since Beto isn't one. Now check Ana: if Ana is a knight, her claim 'Beto is a knave' must be true, and it is, since we just established Beto is a knave. Everything is consistent: Ana is a knight, Beto is a knave.
Practice Deductive Reasoning
- Deductive Reasoning I · 12 questions · Difficulty 2 out of 5
- Deductive Reasoning II — Knights & Knaves · 12 questions · Difficulty 4 out of 5
- Deductive Reasoning III — Chained Syllogisms · 12 questions · Difficulty 3 out of 5
- Deductive Reasoning IV — Elimination Puzzles · 12 questions · Difficulty 4 out of 5
- Deductive Reasoning V — Hat Puzzles and Common Knowledge · 12 questions · Difficulty 5 out of 5
- Deductive Reasoning VI — Recreational Arithmetic Puzzles · 12 questions · Difficulty 4 out of 5
- Deductive Reasoning VII · 12 questions · Difficulty 3 out of 5
- Deductive Reasoning VIII · 12 questions · Difficulty 4 out of 5