TMUA · Paper 2: Mathematical Reasoning

Self-referential statements and logic puzzles

7 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 7 questions

  1. Consider these three statements. S1: At least one of S2 and S3 is false. S2: S1 is true. S3: S1 and S2 are both false. Which of the statements are true?
  2. Consider these three statements. S1: S2 and S3 are both false. S2: S1 is true or S3 is true. S3: Exactly one of S1 and S2 is true. Which of the statements are true?
  3. Consider these three statements. S1: Exactly one of S2 and S3 is true. S2: Exactly one of S1 and S3 is true. S3: Neither S1 nor S2 is true. Which of the statements are true?
  4. Consider these four statements. S1: Exactly one of these four statements is true. S2: Exactly two of these four statements are true. S3: Exactly three of these four statements are true. **…
  5. Consider these four statements. S1: S2, S3 and S4 are all true. S2: Exactly two of these four statements are true. S3: S1 is false. S4: S2 and S3 have the same truth value. Which of th…
  6. On an island, knights always tell the truth and knaves always lie. Person A says: 'B is a knave.' Person B says: 'A and I are the same type.' What are A and B?
  7. Consider these four statements. S1: Exactly one of S2 and S3 is true. S2: S3 is true and S4 is false. S3: S1 is true or S4 is true. S4: S2 is false. Which of the statements are true?

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