📘 set theory

1. The problem is to simplify the set expression $$A \cup B \cap A$$. 2. Recall the order of operations in set theory: intersection ($\cap$) is performed before union ($\cup$).

1. Let's start by stating the problem: understanding the difference between elements and subsets in set theory. 2. An **element** is a single object or member contained within a se

1. The problem is to understand the difference between elements and sets. 2. In mathematics, a **set** is a collection of distinct objects, considered as an object in its own right

1. **State the problem:** We have 460 people surveyed. 100 read no newspaper, so 360 read at least one of the three newspapers: Daily Times (DT), Guidance (G), and Punch (P). Given

1. **Problem Statement:** In a survey of 120 people, the numbers of people reading Computer (C), Electronics (E), and Mechanics (M) are given along with their intersections. We nee

1. **Problem Statement:** Given the universal set $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ and subsets: $$A = \{x \in U : x \text{ divides } 9\} = \{1, 3, 9\}$$

1. **Problem:** Write the set $\{0,1,2,3,\ldots,10\}$ in set builder notation. 2. **Formula and rules:** Set builder notation describes a set by a property that its members satisfy

1. **Problem statement:** Given a survey of 25 students with preferences for three modules: Communication Skills (CS), Introduction to ICT (ICT), and Mathematics for Computing I (M

1. **Problem Statement:** We are given two sets: $$X = \{1,6,2,3,14\}$$

1. The problem asks us to determine which statements about the set $$A = \{ \text{tiger}, w, \text{cross} \}$$ are true. 2. Recall the definitions:

1. **List the members of the following sets:** (i) Set defined by $x + 3 = 9$.

1. **List the members of the following sets:** (i) Set defined by $x + 3 = 9$.

1. **Problem Statement:** Given sets $P = \{2,3,5,7\}$ and $E = \{2,4,6,8,10\}$, find the union and intersection of $P$ and $E$.

1. **Problem Statement:** You are given two disjoint sets P and Q within a universal set U. You need to represent this information in a Venn diagram.

1. **Problem Statement:** Given $r = 1.38$ cm and $\pi = 3.142$, find the value of $h$ to the nearest first decimal place using logarithm tables. 2. **Understanding the problem:**

1. **Problem Statement:** Represent the information that sets P and Q are two disjoint sets in a universal set using a Venn diagram.

1. Let's clarify the problem: You have two sets and you found their union, which means all elements that are in either set or both. 2. The next step is to find what isn't in the un

1. **State the problem:** We have the universal set $\xi = \{x \mid x \text{ is a prime number between 1 and 15}\}$, sets $A = \{3, 7, 11\}$ and $B = \{2, 5, 7\}$. We want to find

1. **State the problem:** We have 120 students in total. Each student plays soccer, gymnastics, or both. 2. **Given data:**

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

1. **State the problem:** We have three sets A, B, and C representing students playing tennis, basketball, and a third sport respectively, with numbers indicating counts in various