Math Problem Statement

How many elements belong to set A and set B?

Solution

The Venn diagram shows two sets, AA and BB, with elements distributed across four regions:

  • Region I: Elements in set AA only = 29
  • Region II: Elements in both set AA and set BB (intersection) = 15
  • Region III: Elements in set BB only = 6
  • Region IV: Elements outside both sets AA and BB (the universal set but not in AA or BB) = 26

The problem asks how many elements belong to both set AA and set BB. This refers to the number of elements in the intersection of AA and BB, which is located in Region II of the Venn diagram.

Thus, the number of elements in both AA and BB is: 15\boxed{15}

Would you like more details or have any other questions?

Here are 5 related questions to expand your understanding:

  1. How would you find the total number of elements in set AA?
  2. How would you calculate the total number of elements in set BB?
  3. What is the total number of elements in the universal set UU?
  4. How would you find the number of elements that are either in set AA or set BB?
  5. What is the difference between the union and intersection of two sets?

Tip: When working with Venn diagrams, remember that the intersection represents elements common to both sets, while the union covers all elements from both sets.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Venn Diagram
Union and Intersection

Formulas

Union of sets A and B: |A ∪ B| = |A| + |B| - |A ∩ B|

Theorems

Principle of Inclusion-Exclusion

Suitable Grade Level

Grades 6-8