Self-Test 02 - Sets

Check your understanding

This self-test lets you check your understanding of Session 02. It is purely formative: nothing is tracked or graded, and nobody sees your answers. Work through the Tasks first, then use this quiz to confirm the ideas have stuck. A wrong answer triggers a 10-second cooldown before you can retry, so think before you click.

1. Let \(T = \{3, 6, 9, 12\}\). Which statement is true?

2. Which list is exactly the set \(\{x \in \mathbb{N} : x^2 \leq 10\}\)?

3. What is \(|\{4, 7, 7, 10, 13\}|\)? Type the number.

Set Operations

4. What is \(\{2, 5, 8\} \setminus \{5, 9\}\)?

5. By De Morgan’s laws, \((A \cap B)^c\) is always equal to which set?

6. In a fleet, \(34\) trucks have a lift gate, \(25\) have a cooling unit, and \(12\) have both. How many trucks have at least one of the two features? Type the number.

Products & Power Sets

7. Let \(A = \{1, 2\}\) and \(B = \{7, 8\}\). Which of the following is an element of \(A \times B\)?

8. A distribution network connects \(5\) depots with \(3\) stores. How many ordered pairs \((\text{depot}, \text{store})\) (i.e. possible delivery routes) are there? Type the number.

9. A tender lists \(4\) optional services, and a client may book any subset of them (including none). How many different selections are possible (i.e. what is \(|\mathcal{P}(A)|\) for \(|A| = 4\))? Type the number.

Sets in Business

10. Let \(L\) = customers with a loyalty card and \(O\) = customers with an open invoice. Which group is \(L \setminus O\)?

11. A batch size \(q\) must satisfy two constraints: the machine allows \(q \in [4, 10]\) and the contract requires \(q \in [8, 14]\). Which interval is the feasible set?

12. Is the statement \(\emptyset \subseteq A\) true for every set \(A\)? Type one word, lowercase.

Well done. You solved every question. You can handle sets, their operations, products and power sets, and are ready for Session 03 on functions.