📘 set theory

1. **Problem Statement:** We are given several sets and asked to express set relations using symbols, analyze subset relations, and find intersections and unions of sets.

1. **Problem statement:** Given the universal set $$\varepsilon = \{x : x \text{ is an odd integer and } 1 \leq x \leq 25\}$$, and sets $$X = \{x : x \text{ is a multiple of } 3\}$

1. **Problem Statement:** Given the universal set $\varepsilon = \{x : -20 \leq x \leq 20\}$ and sets $M = \{x : -20 < x < 15\}$,

1. Problem 13: Given sets 𝜀 = {x : -20 ≤ x ≤ 20}, M = {x : -20 < x < 15}, N = {x : -10 < x ≤ 10}, P = {x : 9 ≤ x < 18}, find: a. M' (complement of M in 𝜀)

1. Problem 13: Given sets \(\varepsilon = \{x : -20 \leq x \leq 20\}\), \(M = \{x : -20 < x < 15\}\), \(N = \{x : -10 < x \leq 10\}\), \(P = \{x : 9 \leq x < 18\}\), find: a. \(M'\

1. **Determine True or False for each statement:** - a. $a \in A$ (Cannot determine without set $A$ definition)

1. **Determine True or False for each statement:** a. $a \in A$ - Without specific info about $A$, cannot confirm; assume True if $a$ is defined in $A$.

1. **State the problem:** We are given multiple set theory questions involving membership, types of sets, set notation, and set operations. 2. **Membership statements (True/False):

1. **Problem Statement:** Solve question 11 (not provided in the prompt). Since question 11 is missing, I cannot solve it directly. 2. **Explanation:** To solve any set theory prob

1. **Problem Statement:** Find the specified sets and their operations for questions 9 and 10. ---

1. **State the problem:** Find the intersection and union of sets \(M = \{1, 3, 5, 7, 9, 11, 13, 15, 17, 19\}\) and \(N = \{3, 6, 9, 11, 13\}\). 2. **Recall definitions:**

1. The problem states the distributive law of set operations: $$p \cap (q \cup r) = (p \cap q) \cup (p \cap r)$$. 2. This law means the intersection of set $p$ with the union of se

1. **State the problem:** We need to find the complement of set $M$ with respect to the universal set $U$, denoted as $M'$. The complement $M'$ consists of all elements in $U$ that

1. The problem asks to find the intersection of sets $M$ and $Z$, denoted as $M \cap Z$. 2. The intersection of two sets contains all elements that are common to both sets.

1. **State the problem:** We are given the total number of elements in the universal set $\xi$ as $n(\xi) = 21$, the number of elements in the union of sets $A$ and $B$ as $n(A \cu

1. The problem states that we have three sets $A$, $B$, and $K$ such that $A \subset K$, $B \subset K$, and $A \cap B = \emptyset$. 2. This means both $A$ and $B$ are subsets of $K

1. The problem is to understand the set notation $A = \{x \in \mathbb{N} : -2 \leq x\}$ and determine what elements belong to this set. 2. Here, $\mathbb{N}$ represents the set of

1. **Problem statement:** In a class of 50 students, 30 like mango, 25 like guava, and 10 like none of the fruits. Find the number of students who like both fruits, mango only, and

1. **Problem Statement:** Describe the shaded regions in the Venn diagram using set notation.

1. **Problem Statement:** We have a survey about people liking apricots (A), bananas (B), and cantaloupes (C) with given counts and intersections. We want to find the number who li

1. **Problem Statement:** Given sets: