📘 set theory

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:**

1. The problem asks to shade specific regions in a Venn diagram with three sets A, B, and C. 2. Recall the set operations:

1. The problem is to generate Venn diagrams, which are graphical representations of sets and their relationships. 2. Venn diagrams typically show all possible logical relations bet

1. The problem asks to shade specific set operations on three overlapping sets A, B, and C inside a universal set. 2. Recall the set operation definitions:

1. Problem: Given sets $A = \{1, 3, 4, a\}$ and $B = \{2, 5, b, c\}$ where $a, b, c$ are digits, and the intersection $A \cap B$ has 2 elements. Also, $a + b + c = 22$. We need to

1. The problem asks to find the union of two sets: $A \cup B$ and $B \cup A$.\n\n2. Recall the definition of union of sets: $X \cup Y$ is the set containing all elements that are i

1. **State the problem:** We need to verify the set equality $$B - A = A^c \cap B$$ using a membership table. 2. **Recall definitions:**

1. **Problem statement:** In a class, 45% offer History, 30% offer Physics, and 40% offer Biology. 11% offer History and Physics, 15% offer Biology and Physics, 10% offer History a

1. **Problem statement:** We are given two sets A and B. - Number of elements in $A \cup B$ is 49.