📘 set theory

1. The problem asks to identify the Cartesian product $A \times B$ from the given options. 2. The Cartesian product $A \times B$ is defined as the set of all ordered pairs $(a,b)$

1. The problem is to understand what a finite set is. 2. A set is a collection of distinct objects, called elements.

1. **State the problem:** We need to find all elements in the intersection of sets $G$ and $H$, where - $G = \{ x : x \text{ is an odd number} \}$

1. **Problem Statement:** We have sets:

1. **State the problem:** We have 800 households and three brands of cooking oils: Rina, Avena, and Elianto. Given data:

1. The problem asks to identify the correct interval or set relation for each question. 2. For question 11: $\mathbb{R}$ is the set of all real numbers, which corresponds to the in

1. **Problem Statement:** Show that for sets $A$, $B$, and $C$, the cardinality of their union satisfies the inclusion-exclusion principle:

1. **Problem Statement:** Given sets \(A = \{0, 2, 4, 6, 8, 10\}\), \(B = \{0, 1, 2, 3, 4, 5, 6\}\), and \(C = \{4, 5, 6, 7, 8, 9, 10\}\), find: c) \(A - B\)

1. Let's define variables based on the problem: - Let $F$ be the number of students who learn the flute.

1. **State the problem:** We have a group of 20 people. Among them, 13 like tea, 12 like coffee, and 3 like neither tea nor coffee. We want to find how many people like tea but not

1. **Problem Q-1:** Given sets $A=\{a,b,c\}$, $B=\{x,y\}$, and $C=\{0,1\}$, find Cartesian products. - a) $A \times B \times C$ is the set of all ordered triples $(a_i,b_j,c_k)$ wh

1. Problem: Describe the regions in Venn diagrams for three sets with eight regions each. 2. For each problem, the three sets form overlapping circles dividing the universal set in

1. The problem states: In a class of 35 students, 29 play cricket, 16 play football, and 10 play both cricket and football. 2. We need to find the number of students who play crick

1. The problem asks for the union of two sets $A$ and $B$, where $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$. 2. The union of two sets $A$ and $B$, denoted $A \cup B$, is the set

1. **State the problem:** We have a class of 40 students. - 25 study Mathematics.

1. Problem: Determine subset relations and equality between sets and elements as given. 2. Analyze each statement:

1. დავწეროთ მოცემული მონაცემები: A = 24, A \cup B = 11, A \cup B \cup C = 40.

1. დავწეროთ მოცემული მონაცემები: $|A|=24$, $|A \cup B|=11$, $|A \cup B \cup C|=40$. 2. დავინახოთ, რომ $|A \cup B|=11$ არ შეიძლება იყოს ნაკლები $|A|=24$-ზე, აქ შეიძლება შეცდომაა, მა

1. **State the problem:** Given the universal set $U = \{x \mid x \in \mathbb{N}, 0 \leq x \leq 9\}$ and sets $A = \{2,4,7,9\}$, $B = \{1,3,5,7,9\}$, $C = \{2,3,4,5\}$, and $D = \{

1. **State the problem:** We have 50 people in total. Among them, 27 know Chinese, 19 know English, and 13 know neither language. We need to find how many people know both Chinese

1. **State the problem:** We are given the number of kids interested in history, nature, and both subjects, and we need to find the total number of kids in the class. 2. **Identify