📘 set theory

1. **Problem statement:** Given sets $$A = \{ 2, \{3\}, \{2,3\}, 4, \{3,4\} \}$$ and

**Exercise 2: Relation on $\mathbb{R}^3$** Given the binary relation $\mathcal{R}$ on $\mathbb{R}^3$ defined by:

1. The set $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ is the set of counting numbers up to 10. 2. The set $C$ is the set of multiples of 3 less than 10, so $C = \{3, 6, 9\}$. The elem

1. **Stating the problem:** We have three sets representing housewives using detergents A, B, and C, with given numbers and intersections. We want to find: a) The number of housewi

1. Statement: We have a total of 140 people. 15 of them like neither TV nor Radio.

1. Let's start with the **definition of a set**: A set is a collection of distinct objects, considered as an object in its own right. 2. Sets are usually denoted by capital letters

1. Олонлогуудын багц нөхцлийг тодорхойлё.\n Нөхцөлүүд: $$\overline{A} \cup \overline{B} = \emptyset,$$ $$X \Delta A = \emptyset,$$ $$B \setminus A \neq \emptyset.$$\n

1. **Problem 1:** In a class of 40 students, 18 are in the Math Club, 15 are in the Science Club, and 7 belong to both clubs. Find how many students are in either club and how many

1. The problem is to show sets $A$ and $B$ on a Venn diagram and understand their elements. 2. Set $A = \{3,5,6,8,9\}$ and Set $B = \{2,3,4,5\}$.

1. The problem asks us to find the union of the two sets $A$ and $B$, where $A = \{3, 5, 6, 8, 9\}$ and $B = \{2, 3, 4, 5\}$. 2. The union of two sets $A$ and $B$, denoted by $A \c