Four persons: P, Q, R and S are in police custody and one of them has committed a crime. They confess as follows:
A. Person P: Q did it.
B. Person Q: S did it.
C. Person R: I did not do it.
D. Person S: Q lied. If exactly one of the statements is false, which of the following is the guilty person.
Pick an option to check yourself, or open the answer below.
Show answer & explanation
Correct answer: B. Q
Explanation
If Q is guilty: P's statement is true, Q's ('S did it') is false, R's is true, and S's ('Q lied') is true — exactly one false. Each other choice of culprit makes two or more statements false.
More Discrete Structures and Optimisation questions
- Consider the primal problem: maximize z = 5x1 + 12x2 + 4x3 subject to x1 + 2x2 + x3 = 10, 2x1 − x2 + 3x3 = 8, x1, x2, x3 ≥ 0. Its dual is:…
- Considering α, β, γ as logical variables, which represent correct equivalences? (A) (α ∧ (β ∨ γ)) ≡ ((α ∧ β) ∨ (α ∧ γ)) (B) (α ∨ β) ≡ ¬α ∨…
- Let ({a, b}, *) be a semigroup where a * a = b. Which hold? (A) a * b = b * a (B) b * b = b
- Let ε = 0.0005 and R_ε be the relation {(x, y) ∈ ℝ² : |x − y| < ε}, interpreted as 'approximately equal'. R_ε is (A) reflexive (B) symmetri…
- Assertion (A): p̄. Reason (R): (r → q̄, r ∨ s, s → q̄, p → q). Choose the correct answer.
- Which of the following are logically equivalent? A. ¬p → (q → r) and q → (p ∨ r) B. (p → q) → r and p → (q → r) C. (p → q) → (r → s) and (p…