📘 set theory

1. **State the problem:** Find the points that belong to the set $$(A \cap B) \cap C^c$$, which means points that are in both sets A and B, but not in C. 2. **Understand the notati

1. **Stating the problem:** We have 25 students studying languages French (F), Spanish (S), and Arabic (A). Some numbers in the Venn diagram are given, and we need to complete it u

1. **Stating the problem:** We have 100 people visiting a gym on Saturday. Among them, 18 attended the spinning class, 10 attended both spinning and circuits classes, and 56 did no

1. **Stating the problem:** We have 80 students in year 11.

1. The problem asks us to determine why the set $A = \{-1, 0, 1\}$ is not a subset of the set $B = \{1, -1, 2, -2\}$. 2. Recall the definition: A set $A$ is a subset of $B$ (writte

1. **State the problem:** We are given sets $A = \{3, 5, 7\}$, $B = \{3, 7\}$, $C = \{5, 7\}$, and $D = \{5, 7, 9\}$. We need to determine which of the subset relations are true: $

1. **State the problem:** We have two sets $A = \{x, y, z, w\}$ and $B = \{x, y\}$. We need to determine which of the following statements are true: - $B \not\subseteq A$

1. **State the problem:** Find the intersection of sets $A = \{11, 7, -5, 12, 1, 2, 3\}$ and $B = \{1, 2, 6, 9, 11\}$. 2. **Recall the definition of intersection:** The intersectio

1. **State the problem:** We have sets $A = \{x, y, z, w\}$, $B = \{x, w\}$, $C = \{z, w\}$, and $D = \{z, w, t\}$. We need to determine which of the following subset relations are

1. **State the problem:** Determine which subset relationships among the sets $A=\{3,5,7\}$, $B=\{3,7\}$, $C=\{5,7\}$, and $D=\{5,7,9\}$ are true. 2. **Recall the definition of sub

1. The problem is to understand the sets $A = \{1, 3, 5\}$ and $B = \{6, 7\}$.\n\n2. Sets are collections of distinct elements. Here, $A$ contains three elements: 1, 3, and 5. Set

1. **State the problem:** We are given the sizes of sets and their union and need to find the size of the intersection of sets A and B. 2. **Given:**

1. **State the problem:** We surveyed 750 students about tattoos and body piercings. Given:

1. **State the problem:** We are given three sets of states: $$K = \{DE, FL, NJ, NY, PA\}$$

1. **State the problem:** We are given the number of people who own a cat but not a dog, own a dog but not a cat, and the total number of people who own a cat or a dog (or both). W

1. The problem involves finding intersections and unions of sets P, Q, X, and Y based on the Venn diagram values. 2. Recall the definitions:

1. **Problem statement:** We have 50 students, each speaks at least one language: English (E), French (F), or German (G). Given: $|E|=30$, $|F|=15$, $|G|=19$, $|E \cap G|=6$, $|E \

1. **State the problem:** We have a Venn diagram showing guests who had ice cream, custard, both, or neither at a wedding. The numbers are: - Ice Cream only: 51

1. **State the problem:** We have 80 students in total.

1. **Stating the problem:** We have a survey about preferences for Newari food (set $N$) and Thakali food (set $T$). Given: 70% like Newari food, 60% like Thakali food, 20% like ne

1. **Problem:** Prove that the relation $R$ on $\mathbb{R} \times \mathbb{R}$ defined by $(a,b) R (x,y)$ iff $a \leq x$ and $b \leq y$ is a partial ordering. 2. **Recall:** A relat