These Year 13 proof by contradiction multiple choice questions check your understanding of proof by contradiction with 10 questions for pupils aged 17-18. Each question has four answers, and the right one is explained as soon as you choose.
Year 13 proof by contradiction multiple choice questions: the 10 questions
What is the first line of a proof by contradiction that \(\sqrt{5}\) is irrational?
The negation of "all prime numbers are odd" is
In the proof that \(\sqrt2\) is irrational, the contradiction is that
Which statement is a valid counterexample to "if \(n\) is prime then \(n+2\) is prime"?
If \(N=2\times3\times5\times7\times11\times13+1=30031\), then
Which of these cannot be proved by giving examples?
If \(x\) is irrational, then \(x+\tfrac12\) is
Which is the correct negation of "\(n^2\) is even"?
Prove \(14m+21n=1\) has no integer solutions: the key fact is that
In the proof of infinitely many primes, which fact leads to the contradiction?
How to use these Year 13 proof by contradiction multiple choice questions
First, read each question carefully before you look at the four answers. Then work the answer out on paper, so that you do not simply guess. After that, read the explanation, even when you are right. If you score less than 7 out of 10, go back to the proof by contradiction lesson.
Finally, practise more with the proof by contradiction worksheet and the quiz. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.
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