📘 set theory

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

1. **State the problem:** Determine which of the given sets are subsets of the set $$A = \{1, \{2, 3, 4\}, \{5, \{6\}\}, 7, 8\}$$. 2. **Recall the definition of subset:** A set $$B

1. **State the problem:** Determine which of the given sets are subsets of the set $$A = \{1, \{2, 3, 4\}, \{5, \{6\}\}, 7, 8\}$$. 2. **Recall the definition of subset:** A set $$B

1. **State the problem:** We are given the set $$B = \{1, \{2, 3\}, 4, \{5, \{6, 7\}\}, 8\}$$ and asked to determine which of the listed elements are members of set $$B$$. 2. **Rec

1. **State the problem:** We are given two sets: $$P = \{4, 13\}$$

1. **State the problem:** We need to find how many patients had allergies or ear infections, but not both. 2. **Identify given data:**

1. **State the problem:** We are given two sets, Tulips and Flowers, with Tulips completely inside Flowers, and we need to write a statement about their relationship using "all," "

1. **State the problem:** We have a universal set $U = \{x \in \mathbb{N} : 1 \leq x \leq 30\}$, and two subsets:

1. **State the problem:** We are given a Venn diagram with three sets A, B, and C, and we need to find the cardinality of the set \((A \cap B) \cup C\). 2. **Recall the formula:**

1. **State the problem:** We are given a Venn diagram with three sets $A$, $B$, and $C$ and their respective cardinalities in each region. We need to find the cardinality of the un

1. **State the problem:** We are given a Venn diagram with three sets $A$, $B$, and $C$ inside a universal set $U$. We need to find the cardinality of $A'$, the complement of $A$,

1. **State the problem:** We need to find the number of students who are on the Prom and Awards Committees, or on the Field Day Committee. 2. **Identify the sets and values from th

1. **State the problem:** We need to find how many students are in exactly one committee based on the Venn diagram data. 2. **Identify the numbers for exactly one committee:** Thes

1. **State the problem:** We are given a Venn diagram with three committees: Prom, Awards, and Field Day. The numbers represent students in each section. We need to find how many s

1. **State the problem:** We need to find how many students are not on the Prom committee. 2. **Identify the numbers related to the Prom committee:**

1. The problem asks for the number of students who are on both the Field Day committee and the Prom committee. 2. From the Venn diagram, the number of students in the intersection

1. **State the problem:** We need to find how many students are on the Awards committee or the Prom committee. 2. **Identify the sets and values from the Venn diagram:**

1. **State the problem:** We need to find the total number of students on the Field Day committee. 2. **Identify the relevant parts of the Venn diagram:** The Field Day committee i

1. **State the problem:** We need to find the total number of students on the Student Council given the numbers in each section of the Venn diagram for three committees: Prom, Awar

1. **State the problem:** We have a Venn diagram showing the number of people who went to Dinner, Movie, or both. We want to find how many people did exactly one activity. 2. **Ide

1. **State the problem:** We have a Venn diagram showing the number of people who went to Dinner, Movie, both, or neither. We want to find how many people did not go to the movies.