Math Problem Statement

Use the Venn diagram and find the elements in the set A ∩ B.

Solution

The question asks us to find the elements in the set ABA \cap B, which represents the intersection of sets AA and BB. The intersection contains elements that are common to both sets.

From the Venn diagram:

  • Elements of set AA include: 4,9,3,6,2,14, 9, 3, 6, 2, 1.
  • Elements of set BB include: 2,8,1,9,72, 8, 1, 9, 7.

The intersection ABA \cap B is represented by the overlapping section of the two circles in the Venn diagram, which includes the numbers that appear in both sets.

The common elements between sets AA and BB are:

AB={9,2,1}A \cap B = \{ 9, 2, 1 \}

So, the answer is:

AB={9,2,1}A \cap B = \{ 9, 2, 1 \}

Would you like more details or have any questions?

Here are some related questions:

  1. How do you find the union of two sets?
  2. What does the complement of a set represent in a Venn diagram?
  3. How can you determine the difference between two sets using a Venn diagram?
  4. How do you represent subsets using Venn diagrams?
  5. What are the properties of set operations such as intersection and union?

Tip: When working with Venn diagrams, always identify which section represents the operation you're interested in (intersection, union, difference, etc.) to find the correct elements.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Intersection of Sets
Venn Diagrams

Formulas

A ∩ B = { x | x ∈ A and x ∈ B }

Theorems

Intersection of Sets

Suitable Grade Level

Grades 5-7