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Mathematics I – foundations – test 2: Sets and mathematical induction

10 multiple-choice and short-answer problems (Mathematics I). The solutions are shown after checking.

For multiple-choice questions choose one answer. For the others type the answer: a number, a decimal or a fraction such as 5/12. When you finish, click Check answers.

1. A={1,2,3,4}, B={3,4,5}. What is A∪B?

2. A={1,2,3,4}, B={3,4,5}. What is A∩B?

3. A={1,2,3,4}, B={3,4,5}. What is A∖B?

4. A={1,2,3,4}, B={3,4,5}. What is the symmetric difference AΔB?

5. How many elements does the power set P(A) have for A={1,2,3}?

6. A has 3 elements and B has 4. How many elements does A×B have?

7. How many elements does A={x∣x∈Z∧−2≤x≤7} have?

8. Which set is C={x∣x∈R∧x2−25=0}?

9. What is the first step of mathematical induction?

10. Induction proves 1+2+⋯+n=n(n+1)2. What is 1+2+⋯+20?