Math Problem Statement

Using the Venn Diagram below, determine the elements of each of the given sets: 4. A ∩ B 5. A ∪ B

Solution

Let's analyze the given Venn Diagram and solve the questions:

4. ABA \cap B (Intersection of A and B)

The intersection ABA \cap B contains elements that are in both sets AA and BB. From the diagram, the overlapping region of AA and BB includes the element:

  • {3}\{3\}

So, AB={3}A \cap B = \{3\}.


5. ABA \cup B (Union of A and B)

The union ABA \cup B contains all elements in either AA or BB or both. From the diagram, ABA \cup B includes:

  • Elements in AA: {2,3,11}\{2, 3, 11\}
  • Elements in BB: {3,5,7}\{3, 5, 7\}

Combining and removing duplicates:

  • AB={2,3,5,7,11}A \cup B = \{2, 3, 5, 7, 11\}

Final Answers:

  1. AB={3}A \cap B = \{3\}
  2. AB={2,3,5,7,11}A \cup B = \{2, 3, 5, 7, 11\}

Would you like detailed explanations or further examples of these concepts?


Here are 5 related questions to expand your understanding:

  1. What is the difference between ABA \cap B and ABA \cup B?
  2. If set UU represents the universal set, what are the elements of AcA^c, the complement of AA?
  3. How would you represent BcB^c, the complement of BB, using this diagram?
  4. Can you identify which elements belong exclusively to AA but not BB?
  5. What would the set AΔBA \Delta B (symmetric difference) look like?

Tip: Always double-check the Venn Diagram regions to correctly categorize elements in set operations!

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Math Problem Analysis

Mathematical Concepts

Set Theory
Venn Diagrams
Set Intersection
Set Union

Formulas

A ∩ B: The intersection of sets A and B, containing all elements common to both sets.
A ∪ B: The union of sets A and B, containing all elements that are in A, B, or both.

Theorems

Basic properties of sets

Suitable Grade Level

Grades 6-8