Math Problem Statement

Which of the following does the Venn diagram represent?

Solution

The Venn diagram in the image represents two sets, AA and BB, inside a universal set UU. Based on the diagram:

  • The yellow region outside of the two circles (representing AA and BB) is the complement of the union of AA and BB, denoted as (AB)c(A \cup B)^c, meaning everything outside of the union of sets AA and BB.

Thus, the diagram represents (AB)c(A \cup B)^c, which includes all elements that are in the universal set UU but not in either AA or BB.

Would you like any further details on how this works?

Here are 5 related questions you can explore:

  1. What is the union and intersection of sets in Venn diagrams?
  2. How is the complement of a set defined in set theory?
  3. What are the common operations in Venn diagrams, such as union, intersection, and difference?
  4. How do you represent the complement of AA and BB individually?
  5. How do you find the area represented by both the intersection and the union in a Venn diagram?

Tip: Always start analyzing Venn diagrams by identifying the universal set and whether the shaded region is inside or outside the sets shown.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Venn Diagrams
Complement of a Set
Union of Sets

Formulas

(A ∪ B)^c

Theorems

Complement Theorem
Union of Sets

Suitable Grade Level

Grades 9-12