Math Problem Statement

Укажите результат операции \(\overline{A}\), учитывая, что имеются только те элементы, которые представлены в множестве \(U\) (от 0 до 9).

Solution

To solve the problem based on the uploaded image, let's analyze the given sets and determine the result for the operation A\overline{A}, which is the complement of AA relative to the universal set UU.

Given 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\}

The complement of AA (A\overline{A}) consists of all elements in UU that are not in AA.

Steps:

  1. Identify all elements of UU: {0,1,2,3,4,5,6,7,8,9}\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}.
  2. Remove elements of A={2,4,6,8}A = \{2, 4, 6, 8\} from UU.

Calculation:

The elements remaining in UU after removing AA are: {0,1,3,5,7,9}.\{0, 1, 3, 5, 7, 9\}.

Result:

The complement of AA is: A={0,1,3,5,7,9}.\overline{A} = \{0, 1, 3, 5, 7, 9\}.

In the required format (numbers without spaces or commas, in ascending order): Answer: 013579\text{Answer: } 013579

Let me know if you need further clarification!


Related Questions:

  1. What is the complement of BB relative to UU?
  2. What is the union of AA and BB?
  3. What is the intersection of AA and CC?
  4. How do you find the difference between two sets (e.g., ABA \setminus B)?
  5. How can we verify if a set is a subset of another?

Tip:

When calculating complements, always work within the universal set UU and exclude the elements explicitly stated in the subset.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Complement of a Set
Universal Set

Formulas

\(\overline{A} = U \setminus A\)

Theorems

Basic Set Theory

Suitable Grade Level

Grades 6-8