Math Problem Statement

Use the given sets to find A ∪ B, where A = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14} and B = {3, 5, 7, 9, 11, 13}.

Solution

To find the union ABA \cup B of two sets AA and BB, you combine all the elements from both sets, ensuring that there are no duplicates.

From the image, we have:

  • A={5,6,7,8,9,10,11,12,13,14}A = \{5, 6, 7, 8, 9, 10, 11, 12, 13, 14\}
  • B={3,5,7,9,11,13}B = \{3, 5, 7, 9, 11, 13\}

The union ABA \cup B contains all elements that are in either set AA or set BB, without repetition. Therefore:

AB={3,5,6,7,8,9,10,11,12,13,14}A \cup B = \{3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\}

Would you like any more details or further explanation?

Here are 5 related questions to extend this topic:

  1. What is the intersection ABA \cap B of the sets AA and BB?
  2. How do you find the difference ABA - B between two sets?
  3. What is the complement of set AA if the universal set is all integers from 1 to 15?
  4. How does the symmetric difference ABA \oplus B work, and what would it be for these sets?
  5. Can you have the union of more than two sets, and how would that work?

Tip: When finding a union of sets, always remove duplicate elements to avoid repetition!

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Math Problem Analysis

Mathematical Concepts

Set Theory
Union of Sets

Formulas

A ∪ B = {x | x ∈ A or x ∈ B}

Theorems

Union Theorem

Suitable Grade Level

Grades 6-8