📘 set theory

1. **Stating the problem:** We have sets $A=\{a,b,c,d\}$ and $B=\{5,7,9\}$ and four relations: A. $f=\{(a,1),(b,2),(c,3),(d,4)\}$

1. **State the problem:** We have Set A as the positive factors of 81 and Set B as the positive multiples of 9. We need to find Set C, which is the intersection of Sets A and B, me

1. **Problem:** Find $B \cup C$ where $B = \{1,3,5,7\}$ and $C = \{3,4,5\}$. 2. **Formula and rules:** The union of two sets $B$ and $C$, denoted $B \cup C$, is the set of all elem

1. **State the problem:** We are given two sets: $$B = \{1, 3, 5, 7, 9, 11, 13, 14\}$$

1. **Problem Statement:** Given a Venn diagram representing students who passed in Mathematics, Science, and Tamil subjects with a total of 80 students.

1. The problem asks to list out the elements of the set of real numbers denoted by the capital letter $\mathbb{R}$. 2. The set $\mathbb{R}$ includes all numbers that can be found o

1. **Problem Statement:** A group of 22 travellers each had at least one of the following: passport (P), health certificate (H), or convertible currency (C).

1. **Problem Statement:** Find the union, intersection, difference of sets A, B, C and verify De Morgan's law using Venn diagrams.

1. **State the problem:** We need to find the number of participants who are university graduates from Ekiti state working in the banking sector. 2. **Given data:**

1. **State the problem:** We have 18 students in the Math Club, 22 students in the Science Club, and 10 students in both clubs. We want to find:

1. **Problem:** Find the union and intersection of the sets $A_n = [3 + \frac{1}{n}, 5 - \frac{1}{n}]$ for $n \in \mathbb{N}$. 2. **Formula and rules:**

1. **Problem statement:** Given sets $U=\{a,b,c,d,e\}$, $A=\{a,b,c\}$, and $B=\{b,c,d,e\}$, verify: (i) $ (A \cup B)' = A' \cap B' $

1. **State the problem:** We have three sets defined with conditions on $x$ and three values a=5, b=8, c=4. We want to find which option (A, B, C, or D) correctly matches the value

1. **State the problem:** We have 120 students surveyed about their preferences for three brands of mineral water: Voltaic, Silver, and Deep. Given the numbers who like each brand

1. **State the problem:** We have a survey of 120 college students who like three brands of mineral water: Voltic, Silver, and Deep. Given the numbers of students who like each bra

1. **State the problem:** There are 100 students in a class. 55 study physics, 50 study French, and 30 study geography. 44 study exactly two of the subjects. We need to find how ma

1. **Problem statement:** There are 90 members in a sports club playing at least one of tennis, football, and volleyball. Given: - Tennis and football players: 10

1. **State the problem:** We have 80 senior five students who passed Math (M). Among them, 45 passed Physics (P), 60 passed Chemistry (C), 5 passed Biology (B), and 5 passed only M

1. The problem is to understand the meaning of the symbol \subseteq in mathematics. 2. The symbol \subseteq means "is a subset of or equal to" in set theory.

1. مسئله: بررسی صحت یا نادرستی گزاره‌های داده شده در مبانی نظریه مجموعه‌ها. 2. برای هر گزاره، باید با استفاده از تعاریف مجموعه‌ها، عضویت ($\in$)، زیرمجموعه ($\subseteq$) و عملیات م

1. **Problem:** Find the intersection of sets $A$ and $B$ where $A = \{1, 2, 3, 4, 5\}$ and $B = \{1, 3, 5, 7, 9\}$. 2. **Formula:** The intersection of two sets $A$ and $B$, denot