Math Problem Statement

Даны множества: U = {0; 1; 2; 3; 4; 5; 6; 7; 8; 9}, A = {2; 4; 6; 8}, B = {2; 3; 4; 5}, C = {1; 3; 5; 7; 9}. Укажите результат операции A ∪ B. В ответе укажите эти числа без пробелов и запятых в порядке возрастания. Если множество пустое, укажите цифру 0.

Solution

We are tasked with finding the union of sets AA and BB, denoted as ABA \cup B. Let’s proceed step by step:

Given Sets:

  • A={2,4,6,8}A = \{2, 4, 6, 8\}
  • B={2,3,4,5}B = \{2, 3, 4, 5\}

Definition of Union (ABA \cup B):

The union of two sets includes all distinct elements from both sets.

Step 1: Combine Elements of AA and BB

Combine all elements: AB={2,4,6,8}{2,3,4,5}A \cup B = \{2, 4, 6, 8\} \cup \{2, 3, 4, 5\}

Step 2: Remove Duplicates and Arrange in Ascending Order

The combined elements are: {2,4,6,8,3,5}\{2, 4, 6, 8, 3, 5\}

Now, sorting them in ascending order: AB={2,3,4,5,6,8}A \cup B = \{2, 3, 4, 5, 6, 8\}

Final Answer (as requested, without spaces or commas):

234568


Do you want me to explain any step in more detail or perform other operations with these sets?

Related Questions:

  1. What is the intersection of AA and BB (ABA \cap B)?
  2. How do we find the union ACA \cup C using the given sets?
  3. What is the difference ABA - B?
  4. What is the complement of BB in the universal set UU?
  5. How would the union of all three sets ABCA \cup B \cup C look?

Tip:

When working with unions, always combine all elements first and then remove duplicates for a clear and sorted result.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Union of Sets
Sorting in Ascending Order

Formulas

Union of Sets: A ∪ B = {x | x ∈ A or x ∈ B}

Theorems

Union of sets property: All distinct elements of both sets are combined.

Suitable Grade Level

Grades 6-8