Math Problem Statement
Given the Venn diagram below with the universal set U and sets A and B, what are the elements of (A ∪ B)'?
Solution
To find the elements of , which is the complement of the union of sets and , we need to follow these steps:
-
Union of and ():
- The union of two sets includes all elements in either , , or both.
- From the Venn diagram:
- Elements in are:
- Elements in are:
- The union
-
Complement of ():
- The complement includes all elements in the universal set that are not in .
- Based on the Venn diagram, the elements outside sets and are .
So, the elements of are .
Thus, the correct answer is:
Do you want more details or have any questions?
Here are 5 related questions to deepen understanding:
- What is the difference between a union and an intersection of two sets?
- How would you find using a similar approach?
- Can you explain how the universal set influences set complements?
- What happens if the sets and are disjoint (have no elements in common)?
- How does the concept of a complement change if the universal set is redefined?
Tip: When dealing with complements, always ensure you know the universal set's elements, as the complement is based on this.
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Math Problem Analysis
Mathematical Concepts
Set Theory
Union and Complement of Sets
Venn Diagrams
Formulas
A ∪ B (Union of sets A and B)
(A ∪ B)' (Complement of union of sets)
Theorems
Basic Set Theory Laws
Complement Rule in Set Theory
Suitable Grade Level
Grades 8-10