📘 set theory

1. The problem asks for the number of pizzas that have chillies on them based on the Venn diagram. 2. According to the Venn diagram, the pizzas that have chillies are the ones insi

1. First, solve the arithmetic expression given: 3 \times 16 \div 3 = ? and 24 \times 8 + ? \div 2. Step 1: Calculate 3 \times 16 = 48.

1. The problem asks to find the power set of the set $\{a,b\}$. 2. Recall, the power set of a set is the set of all its subsets, including the empty set and the set itself.

1. The problem asks us to find the power set of the set $\{a\}$. 2. The power set of a set is the set of all possible subsets of the original set, including the empty set and the s

1. The problem involves finding the cardinality $n(X \times Y)$ and related values from given cardinalities. 2. Recall the rule for Cartesian products cardinalities: $$n(X \times Y

1. The problem asks for the meaning of the set \(\{(x,y) : x \in A, y \in B\}\). This is by definition the Cartesian product \(A \times B\), the set of all ordered pairs where the

1. Problem statement: Given sets \(A=\{5, 10, 15, 20, 25\}\), \(B=\{5, 25, 125, 625\}\), and universal set \(U = A \cup B\), find: i) Elements of \(U\)

1. **State the problem:** We have two sets: - $A = \{x \mid x \text{ is an even number less than } 10\}$

1. Stating the problem: Given the set $$A = \{ \{ c, a, r \}, \text{taxi} \},$$ determine which of the following are true: (Choice A) $$a \in A$$

1. **State the problem:** We have a set $$A = \{1, \{2, 3\}, 4, 5\}$$ and need to determine which of these statements are true: - (A) $$\{2, 3\} \in A$$

1. **State the problem:** Given the set $$A = \{ \text{b, c, d}, \{ \text{a, e} \} \}$$, we need to determine which of the following statements are true.

1. Problem: Given the set $A = \{ 5, \{6, 7\}, 8 \}$, determine which of the following statements are true: (Choice A) $\{6, 7\} \subset A$

1. The set is defined as $$A = \{ \{\text{x, 1}\}, \{\text{y, 2}\}, \{\text{z, 3}\} \}.$$ 2. To evaluate the truth of each statement, let's analyze each carefully:

1. **State the problem:** We have 136 boys who play rugby, soccer, or hockey. Given the counts for each sport and their pairwise overlaps, we want to find how many boys played all

1. **Stating the problem:** Given the universal set $$U = \{1, 2, 3, ..., 11\}$$, and sets $$A = \{1, 3, 5, 7, 11\}$$ and $$B = \{3, 5, 7, 9\}$$, we want to find:

1. مسئله را بیان می‌کنیم: نوشتن صورت ریاضی و اعضای مجموعه‌های ارائه شده و نمایش اجتماع دو مجموعه A و B. 2. مجموعه اعداد حسابی (W) تعریف شده as

1. The problem asks us to illustrate given information on a Venn diagram. 2. Since no specific sets or elements are provided, we cannot draw a specific Venn diagram.

1. **State the problem:** In a class of 36 students, 19 read biology, 16 read chemistry, and 5 students do not read either subject. Find how many students read both biology and che

1. Stating the problem: Identify which sets among A, B, C, D, E, F, G, H are equal. Step 1: Solve equations for A and B.

1. You requested Venn diagrams for each question. 2. Since no specific mathematical problem involving sets or Venn diagrams was provided, I cannot generate corresponding diagrams o

1. Problem 26: Draw Venn diagrams for the sets A, B, and C with following expressions: a) $A \cap (B \cup \overline{C})$