Math Problem Statement

B AND C

B AND C

Solution

The image shows a Venn diagram with three sets: CC, BB, and MM. The numbers within the diagram represent the elements in various regions corresponding to the intersections of these sets. Let's analyze the sets:

  1. Set CC contains:

    • Only in CC (not in BB or MM): 1313
    • In CBC \cap B: 55
    • In CMC \cap M: 66
    • In CBMC \cap B \cap M (the intersection of all three sets): 44
  2. Set BB contains:

    • Only in BB (not in CC or MM): 2020
    • In BCB \cap C: 55
    • In BMB \cap M: 22
    • In BCMB \cap C \cap M: 44
  3. Set MM contains:

    • Only in MM (not in BB or CC): 3030
    • In MCM \cap C: 66
    • In MBM \cap B: 22
    • In MBCM \cap B \cap C: 44

In summary:

  • The total number of elements in CC: 13+5+6+4=2813 + 5 + 6 + 4 = 28
  • The total number of elements in BB: 20+5+2+4=3120 + 5 + 2 + 4 = 31
  • The total number of elements in MM: 30+6+2+4=4230 + 6 + 2 + 4 = 42

If you want any further details or have specific questions about the set relationships, feel free to ask!


Here are some related questions for further understanding:

  1. What is the union of all three sets CBMC \cup B \cup M?
  2. How many elements are common to both BB and CC but not in MM?
  3. What is the number of elements that belong to both BB and MM?
  4. What is the total number of elements present in the diagram?
  5. How many elements belong only to CC?

Tip: Venn diagrams are a great visual tool to analyze relationships between sets and identify intersections, unions, and differences.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Venn Diagrams
Intersection of Sets

Formulas

n(A ∩ B): Number of elements common to both sets A and B

Theorems

Intersection Theorem: Elements that are common to both sets A and B are found in their intersection.

Suitable Grade Level

Grades 6-8