Logical Deduction Problems Flashcards

A survey shows: everyone who jogs also stretches. Half of those who stretch also lift weights. Tom jogs. What must be true about Tom?

Answer: Tom stretches

Jogging guarantees stretching, but whether Tom also lifts weights is not certain from 'half' — only stretching is guaranteed.

In a race, P finished before Q. R finished after S. S finished before P. What is the correct finishing order?

Answer: S, P, R, Q

S before P before Q is fixed; R is after S but the constraints allow R after Q, giving S, P, Q, R or S, P, R, Q — the only fully consistent order with all constraints is S, P, R, Q.

No herbivores eat meat. Cows are herbivores. Bessie is a cow. Which conclusion is valid?

Answer: Bessie does not eat meat

Bessie is a cow, cows are herbivores, and no herbivores eat meat — so Bessie does not eat meat.

Exactly one of these three people is lying: Alex, Blake, Chris. Alex says 'I am telling the truth.' Blake says 'Alex is lying.' Chris says 'Blake is lying.' Who is lying?

Answer: Blake

If Blake is the liar, Alex tells truth (consistent), and Chris tells truth about Blake lying — exactly one liar, so Blake is the liar.

A committee selects members under this rule: if X is chosen, Y must also be chosen. Y was not chosen. What can you conclude?

Answer: X was not chosen

By contrapositive, if Y is not chosen, then X cannot be chosen.

All squares are rectangles. Figure Z is not a rectangle. Which conclusion must follow?

Answer: Figure Z is not a square

Since every square is a rectangle and Z is not a rectangle, Z cannot be a square.

Five items are ranked 1–5 (1 = best). Item M ranks higher than N. Item O ranks lower than P. P ranks higher than M. Which item is ranked 1st?

Answer: P

P ranks higher than M, and M ranks higher than N — P is the highest in its chain, so P is ranked 1st.