📘 set theory

1. **State the problem:** Find how many boys in a class of 20 are simultaneously tall, play soccer, wear watches, and wear brown shoes. 2. **Given data:**

1. **Stating the problem:** We want to understand the different types of sets in mathematics, their definitions, and examples. 2. **Definition and types of sets:**

1. **Problem Statement:** We have a table of 231 employees classified by job category (B1 to B6) and age category (A1 to A5). We need to explain and find the number of employees in

1. **Problem statement:** A department store surveyed 1603 shoppers.

1. **State the problem:** We have a survey with adults watching two programs: the Big Game and the New Movie.

1. **State the problem:** We are given data about ownership of laptops, cell phones, and tablets from a survey. We need to find: - The percent of people who owned a cell phone.

1. **State the problem:** We have 980 married women surveyed about having a career and/or a child. Given data:

1. The problem is to match the shaded region in each Venn diagram with the correct set expression from the given list. 2. The expressions describe unions, intersections, complement

1. Describe the following sets in words: 1.a The set \{2, 4, 6, 8\} consists of the first four positive even numbers.

1. **State the problem:** Given a universal set $U$ with $n(U) = 119$, and two subsets $A$ and $B$ with $n(A) = 70$, $n(B) = 48$, and $n(A \cup B) = 103$, find the number of elemen

1. **State the problem:** Given the universal set size $n(U) = 144$, the size of set $A$ is $n(A) = 46$, the size of set $B$ is $n(B) = 83$, and the size of the union $n(A \cup B)

1. **State the problem:** We have the universal set $U$ as the months of the year: \{January, February, March, April, May, June, July, August, September, October, November, Decembe

1. **State the problem:** We are given a table of animal counts by class and time of highest activity. We need to find the cardinal numbers of the sets:

1. The problem is to draw a Venn diagram with 3 sets showing their union. 2. A Venn diagram with 3 sets consists of three overlapping circles, each representing a set.

1. Let's consider two sets with numbers to understand Venn diagrams better. 2. Suppose set $A = \{1, 2, 3, 4\}$ and set $B = \{3, 4, 5, 6\}$.

1. Let's start by understanding what a Venn diagram is. 2. A Venn diagram is a visual tool used to show the relationships between different sets.

1. The problem is to find the union of two sets and illustrate it with a Venn diagram. 2. The union of two sets $A$ and $B$ is defined as the set containing all elements that are i

1. The problem is to draw a Venn diagram, which is a visual representation of sets and their relationships. 2. Venn diagrams typically show all possible logical relations between a

1. **Problem:** Find $A \cup B \cup C$ where $A = \{1, 2, 4, 8\}$, $B = \{2, 4, 6, 8\}$, $C = \{1, 2, 3, 4\}$.

1. **State the problem:** Given sets $U = \{1, 2, 3, 4, 5\}$, $X = \{2, 4\}$, and $Y = \{1, 3, 4\}$, find: - $X \cap Y$

1. **State the problem:** We are given a set $A = \{1, 2, 3\}$ and asked two questions about its power set $P(A)$. 2. **Number of elements in the power set:** The power set of a se