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

This University logic, sets and proof techniques test lasts 60 minutes and is marked out of 20. It covers the whole chapter for pupils aged 18-19, and the full answers are on a separate page.

⏱️ Duration : 60 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Negation and contrapositive
1. Write the negation of "For every real \(x\) there is a real \(y\) with \(y>x\)". (2 marks)
2. State the contrapositive of "If \(n\) is divisible by 6, then \(n\) is even". (2 marks)
Question 2 – Sets and counting
In a group of 50 people, 30 speak French, 22 speak Spanish and 10 speak neither.
1. How many speak both languages? (3 marks)
2. How many speak exactly one language? (1 mark)
Question 3 – A direct proof
Prove that the sum of three consecutive integers is divisible by 3.
Question 4 – Proof by contradiction
Prove that there is no largest prime number.
Question 5 – Induction
Prove by induction that \(\displaystyle\sum_{i=1}^n(2i-1)=n^2\) for all \(n\ge1\).

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

First, revise with the logic, sets and proof techniques lesson and the worksheet. Then sit the test in one go, with a timer set to 60 minutes. After that, mark your work with the logic, sets and proof techniques test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this University logic, sets and proof techniques test as a PDF and print it like a real exam paper. 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.

Logic, sets and proof techniques – university Year 1 maths test to download as PDF

Question 1 – Negation and contrapositive

Question 2 – Sets and counting

Question 3 – A direct proof

Question 4 – Proof by contradiction

Question 5 – Induction

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

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