📘 set theory

1. **Problem:** Given sets $A = \{a, b, c, d, e\}$ and $B = \{a, b, c, d, e, f, g, h\}$, find: (a) $A \cup B$

1. **Problem:** In a class of 80 students, every student studies Economics and Geography on both. If 65 students study Economics and 50 study Geography, how many study both subject

1. Problem: Determine the nature of the set $A = (2,4,6,8,10, \ldots)$. - This set contains even numbers starting from 2 and continues indefinitely.

1. The problem asks to identify the type of set A = {2,4,6,8,10, ...}. 2. This set contains even numbers starting from 2 and continues indefinitely.

1. The problem is unclear as the input is just the symbol \in, which is used in mathematics to denote "element of" in set theory. 2. Typically, \in is used to express that an eleme

1. **Stating the problem:** We have 100 students in total.

1. The problem involves identifying the shaded region in a Venn diagram with three sets $P$, $Q$, and $R$ within the universal set $\xi = P \cup Q \cup R$. 2. The shaded region is

1. مسئله: یافتن اشتراک دو مجموعه $A = (-\infty, 2]$ و $B = (-1, 5]$ است. 2. تعریف اشتراک: اشتراک دو مجموعه $A \cap B$ شامل تمام عناصری است که در هر دو مجموعه وجود دارند.

1. مسئله: مجموعه $A = \{\emptyset, \{1\}, \{2\}, \{1, \{2\}\}, \{\emptyset\}\}$ را در نظر بگیرید. الف) تعداد اعضای مجموعه $A$ را بیابید. 2. برای شمارش اعضای مجموعه، هر عضو را جداگا

1. **State the problem:** We are given two sets $P = \{a, b, c, d, e\}$ and $R = \{t, d, c, b, e\}$. We need to find the set difference $P - R$. 2. **Formula and explanation:** The

1. **Problem:** Compute the union and intersection of given sets and other set operations. Given sets:

1. **Problem:** Compute $A \cup B$ where $A = \{a, b, c, g\}$ and $B = \{d, e, f, g\}$. 2. **Formula:** The union of two sets $A$ and $B$ is defined as $A \cup B = \{x : x \in A \t

1. The problem states: "B is a set of days of the week that starts with A." We need to understand what this means. 2. The days of the week are: Monday, Tuesday, Wednesday, Thursday

1. **Problem:** Find the total number of elements in the power set of a set $A$ containing 15 elements. 2. **Formula:** The power set of a set with $n$ elements has $2^n$ elements.

1. **Problem:** Find the total number of elements in the power set of a set $A$ containing 15 elements. 2. **Formula:** The power set of a set with $n$ elements has $2^n$ elements.

1. **Stating the problem:** We want to prove De Morgan's law for sets, which states that the complement of the union of two sets $A$ and $B$ is equal to the intersection of their c

1. مسئله: تعداد اعضای مجموعه $[A-(B\cup C)]\cup B$ را بیابید که در آن $$A=\{1,4,5,7\},\quad B=\{3,4,6,8\},\quad C=\{1,3,5,7,9\}$$

1. مسئله: ثابت کنید $$A - (A \cap B) = A - B$$. 2. تعریف‌ها و فرمول‌ها:

1. பிரச்சினையை விளக்குதல்: இந்த வென்விருப்படத்தில் இரண்டு வட்டங்கள் உள்ளன: இடது வட்டம் "குடை உள்ள பிள்ளைகள்" மற்றும் வலது வட்டம் "பெண் பிள்ளைகள்".

1. The problem asks us to determine the correct relationship between two sets $A$ and $B$ among the options given: 2. Recall the definitions:

1. **Stating the problem:** We have two sets $A$ and $B$.