TMUA · Paper 2: Mathematical Reasoning

Implications, converses and negations

15 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 15 questions

  1. Consider the statement: 'If a whole number is divisible by 6, then it is divisible by 3.' Which of the following is its contrapositive?
  2. Consider the statement: 'If a quadrilateral is a square, then all four of its sides are equal.' Which of the following is its converse?
  3. Which of the following is the negation of the statement 'If it rains, then the match is cancelled'?
  4. For an integer , the statement is *' is even or '*. Which of the following is its negation?
  5. Which of the following is the negation of *''*, where is a real number?
  6. Which of the following means the same as 'You can vote only if you are registered'?
  7. Which of the following means the same as 'A whole number is divisible by 5 if it ends in 0'?
  8. The lamp is on if and only if the switch is up. Which of the following says the same thing?
  9. It is not the case that both the bus is late and the train is late. Which of the following says the same thing?
  10. Neither the first number nor the second number is prime. Which of the following says the same thing?
  11. In which situation is the statement 'If the alarm sounds, then everyone leaves the building' false?
  12. Which of the following is the contrapositive of 'If a number is divisible by 6, then it is even or a multiple of 9'?
  13. Which of the following is the contrapositive of *'If is irrational, then is irrational'*?
  14. Which of the following is the contrapositive of *'If is even, then is even'*?
  15. Which of the following is logically equivalent to *'Either is not a multiple of 4, or is even'* (for whole numbers )?

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