📘 set theory

1. **Problem Statement:** Find the union of sets $A$ and $B$ where $A = \{0, 4, 8, 12\}$ and $B = \{0, 3, 6, 9, 12\}$. 2. **Formula and Explanation:** The union of two sets $A$ and

1. **Problem Statement:** Find the intersections and unions of the given sets. 2. **Recall the definitions:**

1. The problem involves finding the union of sets $A$ and $Y$, denoted as $A \cup Y$. 2. Recall that the union of two sets $A$ and $Y$ is the set containing all elements that are i

1. ปัญหาคือการหาว่าส่วนที่แรเงาในแผนภาพ Venn ของเซต A, B, C และ U แทนเซตใดในตัวเลือกที่ให้มา 2. เรามีเซต U เป็นเอกภพสัมพัทธ์ และ A, B, C เป็นสับเซตของ U

1. **State the problem:** Find the intersections and unions of given sets. 2. **Recall set operations:**

1. ปัญหาคือหาจำนวนสมาชิกของเซต $P(P(A)) \cup P(A)$ โดยที่ $A = \{\emptyset, \sqrt{2}\}$ 2. เริ่มจากหาขนาดของเซต $A$ ซึ่งมีสมาชิก 2 ตัว คือ $\emptyset$ และ $\sqrt{2}$ ดังนั้น $|A| =

1. **Problem Statement:** We have a Venn diagram with three circles A, B, and C containing various colored shapes. We need to:

1. **Problem Statement:** Prove that for the sets

1. **State the problem:** Given sets A and B with $n(A) = 17$, $n(A \cup B) = 38$, and $n(A \cap B) = 2$, find $n(A - B)$, $n(B)$, and $n(B - A)$. 2. **Recall formulas and rules:**

1. **Problem statement:** Given sets $U = \{x \mid x \in \mathbb{N}, x \leq 10\}$,

1. **Problem Statement:** We are given that 30 students like Maths, 25 like Science, and 10 like both Maths and Science. We need to find how many students like only Maths. 2. **For

1. **Problem statement:** In a class, 65% of students like green (G), 45% like blue (B), and some like both. We need to find the percentage who like both colors. 2. **Formula used:

1. **State the problem:** We have 100 voters choosing among three candidates: Akayuure (A), Manukre (M), and Odonti (O). We want to find the number of voters who preferred all thre

1. **Stating the problem:** We are given sets defined by intervals:

1. **Stating the problem:** We are given sets defined as intervals:

1. **Stating the problem:** We have sets defined as intervals: - $u = \{x : -2 \leq x \leq 5\}$

1. Problem 1: Given the numbers of students in various subject combinations, find the following using a Venn diagram for Nursing (N), Business (B), and Computer (C). 2. i. All thre

1. **Problem Statement:** Prove the set identity $$(A \cup B) \cap (A \cup C) = A \cup (B \cap C)$$ where $A$, $B$, and $C$ are subsets of a universal set $U$. 2. **Recall the dist

1. **Problem Statement:** Prove that $$A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$$. 2. **Formula and Important Rules:**

1. The problem states that $Q \subseteq (\mathbb{R} - \mathbb{Z})$, meaning the set $Q$ is a subset of the real numbers excluding the integers. 2. This implies every element $q \in

1. **Problem Statement:** Prove the set identity $$(A \cup B) \cap (A \cup C) = A \cup (B \cap C)$$ where $A$, $B$, and $C$ are subsets of a universal set $U$. 2. **Formula and Rul