📘 set theory

1. **State the problem:** We are given four pairs of sets (a), (b), (c), and (d). For each pair, we need to determine the relationship between the sets using the options: - Equival

1. **Problem Statement:** Determine if each given set is finite or infinite. If finite, find its cardinality. 2. **Set (a):** $\{1, 2, 3, \ldots, 30\}$

1. **State the problem:** We have a Venn diagram with three sets: S (sheep), C (cows), and P (pigs). The numbers inside represent farms raising those animals. We want to find how m

1. **State the problem:** We have three sets: - Universal set $\xi = \{x : x \text{ is an integer and } 1 \leq x \leq 6\}$

1. **State the problem:** We need to find the number of elements in the intersection of sets $K$, $L$, and $M$, where: - $K$ is the set of multiples of 3.

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: $