University logic, sets and proof techniques quiz to download as PDF

This University logic, sets and proof techniques quiz has 10 short questions for pupils aged 18-19. Type your answer, check it straight away and read the explanation when you get one wrong.

University logic, sets and proof techniques quiz: the 10 questions

Negate \(\exists x\,P(x)\).
How many elements does \(\mathcal P(\{1,2,3\})\) have?
What is \(|A\cup B|\) if \(|A|=7,|B|=5,|A\cap B|=2\)?
Which proof technique shows \(P\Rightarrow Q\) by proving \(\neg Q\Rightarrow\neg P\)?
True or false: the converse of a true statement is always true.
Sum \(1+2+\cdots+100\).
Is \(f(x)=2x+1\) from \(\mathbb R\) to \(\mathbb R\) bijective?
How many equivalence classes does congruence mod 5 give on \(\mathbb Z\)?
What is \(A\setminus A\)?
In induction, what must you prove first?

How to use this University logic, sets and proof techniques quiz

First, answer every question without a calculator unless the question says so. Then check your answer and read the short explanation. If you get fewer than 7 right, revise the logic, sets and proof techniques lesson and try again later. After that, try the multiple choice questions or the logic, sets and proof techniques worksheet.

Finally, take this quiz again before a test, because quick retrieval helps you remember. 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.