📘 set theory

1. **State the problem:** Prove that $ (A \cup B) - (A \cap B) = (A - B) \cup (B - A) $. 2. **Recall definitions:**

1. **State the problem:** There are 80 men in a club, each playing at least one game: football, hockey, or baseball. Given: 20 play only football, 19 play only hockey, 22 play only

1. **Problem Statement:** In a country club of 144 people, 61 play football, 65 play baseball, and 72 play hockey. 22 play all three games, and 11 play none. We need to find: (i) H

1. **State the problem:** There are 80 men in a club, each playing at least one game: football, hockey, or baseball. Given: 20 play football only, 19 play hockey only, 22 play base

1. **State the problem:** Prove that $ (A \cup B) - (A \cap B) = (A - B) \cup (B - A) $. 2. **Recall definitions:**

1. **Problem Statement:** In a country club of 144 people, 61 play football, 65 play baseball, and 72 play hockey. 22 play all three games, 11 play none, and an equal number play o

1. **Problem Statement:** There are 80 men in a club, each playing at least one game among football, hockey, and baseball. Given:

1. **State the problem:** We are given a set $B = \{1, 2, 3, 4\}$ and need to find how many subsets can be formed from this set. 2. **Formula used:** The number of subsets of a set

1. **Problem statement:** Prove that if $R$ is reflexive, then $R$ is symmetric only if for every $a \in A$, whenever $(a,a) \in R$, it implies $(a,a) \in R$ always (which is trivi

1. The user asks to represent "it" on a Venn diagram and explain it, but no specific problem or set information was provided. 2. To create a Venn diagram, we need details about the

1. **Problem statement:** We have 40 teens who watched Harry Potter. - 22 saw it on DVD

1. **State the problem:** We have 35 students in total. - 18 students play hockey.

1. **State the problem:** Prove the identities using algebraic laws of sets: (i) $ (A \cup B) \cap (A \cup B^c) = A $

1. The problem is to understand and solve questions related to set operations such as union, intersection, difference, and complement. 2. Important formulas and definitions:

1. **Problem Statement:** (a) Determine which function from the given options is bijective between sets $P = \{10, 20, 30\}$ and $Q = \{5, 10, 15, 20\}$.

1. **Problem statement:** Given the universal set $\varepsilon = \{x : x \text{ is a positive integer}\}$, and sets $P = \{x : x < 9\}$ and $Q = \{x : x > 4\}$, we need to: a. List

1. **Problem Statement:** Given sets \( \varepsilon = \{p, q, r, s, t, u, v\} \), \( A = \{p, q, r, s\} \), \( B = \{r, t, u, v\} \), and \( C = \{v, s, u, v\} \), find: a. \( n(A

1. **Problem Statement:** Given the universal set $\varepsilon = \{x : x \text{ is a positive integer and } 5 \leq x \leq 40\}$, and sets: - $P = \{x : x \text{ is a multiple of }

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. **Problem statement:** Given sets \(\epsilon = \{x : -20 \leq x \leq 20\}\), \(M = \{x : -20 < x \leq 15\}\), \(N = \{x : -10 < x \leq 10\}\), and \(P = \{x : 9 \leq x < 18\}\),

1. **Problem Statement:** We are given sets and asked to represent sets with symbols, analyze set relations, and find intersections, unions, and complements of sets. 2. **Set Repre