📘 set theory

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.

1. The problem asks: How many people went to dinner and did not go to the movies? 2. From the Venn diagram, the numbers represent:

1. **State the problem:** We are given a Venn diagram with two sets: Dinner and Movie. The numbers represent people who went to Dinner only (16), Movie only (20), both Dinner and M

1. **Problem Statement:** We are given a Venn diagram with two sets: Dinner and Movie. The numbers represent the number of people in each region: - Only Dinner: 16

1. **State the problem:** We have 65 students studying at least one of Geography (G), History (H), and Religious Studies (R).

1. **State the problem:** We have 65 Year 11 students studying at least one of Geography (G), History (H), and Religious Studies (R). Given the numbers in each region of the Venn d