📘 set theory

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

1. **Problem 3:** Given a Venn diagram with universal set $\varepsilon = 350$, $n(C) = 200$ (families owning a car), $n(M) = 120$ (families owning a motor-cycle), and subsets label

1. **State the problem:** We need to place the numbers 28, -43, 19, -8.09, and 4/5 into a Venn diagram with three nested sets: Whole numbers inside Rational numbers inside Integers

1. The problem is to understand the symbol \(\emptyset\), which represents the empty set in mathematics. 2. The empty set is a set that contains no elements.

1. The problem asks to list all subsets of the set $\{1, 2\}$.\n\n2. A subset is any combination of elements from the original set, including the empty set and the set itself.\n\n3

1. The problem asks whether the statement $\{0\} = \emptyset$ is true or false. 2. Recall that $\emptyset$ is the empty set, which means it contains no elements.

1. The problem asks to find the value of $n(A \cup B)$ given $n(A) = 7$, $n(B) = 12$, and $n(A \cap B) = 6$. 2. The formula for the union of two sets is:

1. **State the problem:** We have two sets:

1. The problem asks to interpret the expression $B' \cup T'$ in the context of pupils playing basketball (B), cricket (C), and tennis (T). 2. Here, $B'$ represents the set of pupil

1. **State the problem:** We are given universal set $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$ and subsets $A = \{1, 2, 3, 4, 5, 10\}$, $B = \{3, 4, 6, 8, 10\}$, and $C = \{4

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