Math Problem Statement

What is the universal set \( U \) in the given Venn diagram?

Solution

From the image, we have a Venn diagram with the universal set UU and two subsets AA and BB. Here is the breakdown of the elements:

  • Set AA contains: {10,46,57}\{10, 46, 57\}
  • Set BB contains: {6,13,20,37,39}\{6, 13, 20, 37, 39\}
  • Elements outside AA and BB but in UU are: {5,18,26,48}\{5, 18, 26, 48\}

To find the complete universal set UU, we list all elements in AA, BB, and the elements outside of both sets:

U={5,6,10,13,18,20,26,37,39,46,48,57}U = \{5, 6, 10, 13, 18, 20, 26, 37, 39, 46, 48, 57\}

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Here are some related questions that might deepen understanding:

  1. What is the union of sets AA and BB?
  2. What is the intersection of sets AA and BB?
  3. How many elements are there in the universal set UU?
  4. Are sets AA and BB disjoint?
  5. What is the complement of set AA within UU?

Tip: When dealing with Venn diagrams, make sure to consider each part of the diagram (inside each set, outside, and overlaps) to fully determine the universal set.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Venn Diagrams

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8