Math Problem Statement

Use the given sets to find A∩B.

A={5,6,7,8,9,10,11,12}

B={3,5,7,9,11,13}

Solution

To find the intersection of sets AA and BB, denoted ABA \cap B, we need to identify the elements that are present in both sets.

Given:

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

Now, let's find the common elements in both sets:

  • Common elements: 5,7,9,115, 7, 9, 11

Thus: AB={5,7,9,11}A \cap B = \{5, 7, 9, 11\}

Let me know if you would like further details or have any questions!

Here are 5 related questions you might explore:

  1. What is the union of sets AA and BB?
  2. How would we find ABA - B (the difference of AA and BB)?
  3. What are subsets and how would we determine if BB is a subset of AA?
  4. How would we express ABA \cup B using only elements from AA and BB?
  5. What is the symmetric difference between AA and BB?

Tip: To check for intersections in larger sets, list elements systematically to avoid missing any.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Intersection of Sets

Formulas

A ∩ B = {x | x ∈ A and x ∈ B}

Theorems

Intersection of Sets

Suitable Grade Level

Grades 6-8