Math Problem Statement

Укажите результат операции \( A \cap B \), учитывая множества: \( U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\} \), \( A = \{2, 4, 6, 8\} \), \( B = \{2, 3, 4, 5\} \). Ответ без пробелов и запятых, если пустое, укажите 0.

Solution

To solve this, we need to compute the intersection of sets AA and BB, denoted as ABA \cap B, within the universal set UU.

Here are the provided sets:

  • U={0,1,2,3,4,5,6,7,8,9}U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}
  • A={2,4,6,8}A = \{2, 4, 6, 8\}
  • B={2,3,4,5}B = \{2, 3, 4, 5\}

Steps:

  1. Intersection Calculation: The intersection of AA and BB, ABA \cap B, contains only elements present in both AA and BB.

    • Elements in AA: 2,4,6,82, 4, 6, 8
    • Elements in BB: 2,3,4,52, 3, 4, 5

    Common elements are 22 and 44.

    AB={2,4}A \cap B = \{2, 4\}

  2. Ensure Result is in Universal Set UU: Since all elements of UU are {0,1,2,3,4,5,6,7,8,9}\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}, the elements 22 and 44 are valid.

  3. Final Answer: Arrange the numbers in ascending order, without spaces or commas: Answer: 24\text{Answer: } 24

Would you like more details or clarifications?


Related Questions:

  1. What is the union of sets AA and BB?
  2. How do we calculate ACA \cap C?
  3. Can you explain the properties of set intersection with examples?
  4. What is the complement of ABA \cap B in UU?
  5. How would the result change if B={4,6,8}B = \{4, 6, 8\}?

Tip:

When performing set operations, always double-check the results to ensure they align with the universal set, if given.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Intersection of Sets

Formulas

Intersection of sets: \( A \cap B = \{x \mid x \in A \text{ and } x \in B\} \)

Theorems

Properties of Set Intersection

Suitable Grade Level

Grades 6-8