Math Problem Statement

Choose the correct answer

Consider the following sets: U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; A = {2, 3}. What is A'?

Solution

The problem asks to find the complement of set AA, denoted AA', with respect to the universal set UU.

We are given:

  • U={1,2,3,4,5,6,7,8,9,10}U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
  • A={2,3}A = \{2, 3\}

The complement of AA, denoted as AA', includes all elements in UU that are not in AA. To find AA', we subtract the elements of AA from UU:

A=UA={1,2,3,4,5,6,7,8,9,10}{2,3}={1,4,5,6,7,8,9,10}A' = U - A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} - \{2, 3\} = \{1, 4, 5, 6, 7, 8, 9, 10\}

None of the answer choices directly match this set, so it appears this question has an error. However, based on the available options:

  • The correct complement of AA is {1,4,5,6,7,8,9,10}\{1, 4, 5, 6, 7, 8, 9, 10\}.

Feel free to let me know if you'd like further details or have any questions!

Here are 5 related questions for more practice:

  1. What is the complement of B={1,4,7}B = \{1, 4, 7\} in U={1,2,3,4,5,6,7,8,9,10}U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}?
  2. How do you find the union of two sets?
  3. What is the intersection of AA and B={4,5,6}B = \{4, 5, 6\}?
  4. Can a complement of a set ever be empty?
  5. What is the cardinality of the universal set UU?

Tip: The complement of a set contains all elements from the universal set that are not present in the original set!

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Math Problem Analysis

Mathematical Concepts

Set Theory
Complement of a Set
Universal Set

Formulas

A' = U - A

Theorems

Complement of a Set

Suitable Grade Level

Grades 7-9