📘 set theory

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

1. **Problem:** Determine if the relation $R = \{(A,B) \in P \times P : A = B\}$ on the power set $P$ of $S = \{2,3,7\}$ is reflexive, symmetric, and/or transitive. 2. **Recall def

1. **State the problem:** We have 200 tennis enthusiasts surveyed about attendance at three grand slam tournaments: Australian Open (A), Wimbledon (B), and US Open (C). Given atten

1. **Rewrite the set** $A = \{x \mid x \in \mathbb{Z}, -5 < x < -2\}$ **in roster form.** The set $A$ contains all integers $x$ such that $x$ is greater than $-5$ and less than $-2

1. **State the problem:** We have 12 pupils in a class. They are asked if they have a brother or a sister. 2. **Given data:**

1. **State the problem:** We have 12 pupils in a class (set $\varepsilon$). Among them, 9 have a brother (set $B$), 7 have a sister (set $S$), and 2 have neither. 2. **Goal:** Find

1. **State the problem:** We have universal set $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$, sets $A = \{3, 5, 7, 10\}$ and $B = \{2, 3, 5, 8, 10\}$. We want to find $(A \cap B)'$ usin

1. The problem is to find the union of three sets: $A$, $B$, and $C$, specifically $(A \cup B) \cup C$. 2. The union of two sets $X$ and $Y$, denoted $X \cup Y$, is the set contain

1. The problem asks to find all numbers in the set $Q \cap R'$ where $Q = \{4, 8, 12, 16, 20, 24\}$ and $R = \{6, 12, 18, 24, 30\}$. Here, $R'$ denotes the complement of $R$ relati

1. **State the problem:** We are given two sets: - $Q = \{\text{positive multiples of } 3 \text{ that are less than } 10\}$

1. The problem is to understand what a subset is in mathematics. 2. A subset is a set where every element in it is also an element of another set.