Math Problem Statement
Which of the following does the Venn diagram represent?
Solution
The Venn diagram in the image represents two sets, and , inside a universal set . Based on the diagram:
- The yellow region outside of the two circles (representing and ) is the complement of the union of and , denoted as , meaning everything outside of the union of sets and .
Thus, the diagram represents , which includes all elements that are in the universal set but not in either or .
Would you like any further details on how this works?
Here are 5 related questions you can explore:
- What is the union and intersection of sets in Venn diagrams?
- How is the complement of a set defined in set theory?
- What are the common operations in Venn diagrams, such as union, intersection, and difference?
- How do you represent the complement of and individually?
- 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