📘 set theory

1. **Problem Statement:** Classify the given statements about set $A = \{1, 2, 3\}$ as true or false. 2. **Statements:**

1. **Problem statement:** Given the set $A = \{1, 2, 3\}$, classify each statement as true or false: $2 \in A$, $3 \subset A$, $\emptyset \in A$, $\{0\} \subset A$, $A \cup \{\empt

1. **Problem statement:** Given the set $A = \{1,2,3\}$, classify each statement as true or false: 2 \in A, 3 \subset A, \emptyset \in A, \{\emptyset\} \subset A, A \cup \{\emptyse

1. The problem is to verify the set identity $B - A = A^c - B$ using a membership table. 2. Recall the definitions:

1. **Problem Statement:** We have a universal set represented by a rectangle and a set B inside it. We need to draw sets A and C such that:

1. **Problem Statement:** We are given two sets \(p\) and \(q\) with \(|p| = 10\) and \(|q| = 15\). We need to find the number of elements in the Cartesian products \(p \times q\),

1. The problem is to represent questions in a Venn diagram. 2. A Venn diagram is a visual tool used to show relationships between different sets.

1. The problem is to understand and explain what a Venn diagram is and how it is used in set theory. 2. A Venn diagram is a visual tool used to show the relationships between diffe

1. **State the problem:** We have two sets A and B within a universal set E with the following information:

1. **Problem statement:** (a)(i) Given sets:

1. **Problem Statement:** We have 32 students studying at least one of French (F), Spanish (S), or German (G). Given counts for each language and their intersections, we need to fi

1. **সমস্যাটি বর্ণনা:** আমাদের কাছে সার্বিক সেট $U = \{x : x \in \mathbb{N} \text{ এবং } x \text{ বিজোড় সংখ্যা}\}$, এবং তিনটি সেট:

1. **Stating the problem:** We need to prove that the complement of the union of two sets $A$ and $B$, denoted as $(A \cup B)^c$, is the region outside both $A$ and $B$ inside the

1. **Problem Statement:** Given sets:

1. **Stating the problem:** We have a total of 25 people surveyed. Among them, some like hockey, some like rugby, and some like neither. The numbers given are 6, 8, and 16, where 1

1. **Problem Statement:** Prove that the set of real numbers is uncountable. 2. **Key Concept:** A set is countable if its elements can be put into a one-to-one correspondence with

1. **Problem Statement:** We have a universal set represented by a rectangle and a set B inside it represented by a circle. We need to draw sets A and C such that:

1. The problem involves understanding the Venn diagram representing two sets, WW and ZZ, and their intersection W \cap Z. 2. In set theory, the intersection of two sets, denoted by

1. The problem asks to describe the relationship between sets $W$ and $Z$ using a Venn diagram. 2. A Venn diagram visually represents sets and their relationships using overlapping

1. The problem shows a Venn diagram with three sets labeled W, X, and Z, and the intersection of all three sets is marked as $W \cap X \cap Z$. 2. The symbol $\cap$ denotes the int

1. **State the problem:** Verify using a membership table that $B - A = A \cap B^c$. 2. **Recall definitions:**