Math Problem Statement
Solution
The image describes a question about set theory, specifically the union and intersection of relations and . It asks which statement regarding the union operation is correct.
Here are the options:
- a.
- b.
- c.
- d.
- e.
Explanation of Key Operations:
- Union (): Combines elements from both sets/relations.
- Intersection (): Includes only elements present in both sets/relations.
- Set Difference (): Removes elements of one set from another.
Analyzing the Options:
- Option a: Incorrect. would result in , not .
- Option b: Correct. The union of a set with its intersection with another set results in the original set, i.e., .
- Option c: Incorrect. Union and set difference do not equal each other in this context.
- Option d: Incorrect. Similar reasoning as in option b, but with the wrong result.
- Option e: Incorrect. Union and intersection are not equal unless the sets are identical.
Conclusion:
The correct answer is b.
Would you like further explanation or details on this?
Here are 5 related questions to expand on this topic:
- How does the set union operation differ from set intersection?
- Can the union of two sets ever equal the intersection of those sets? Under what conditions?
- How does the complement of a set relate to the union and intersection operations?
- What is the distributive property of sets with respect to union and intersection?
- How do Venn diagrams visually represent union, intersection, and set difference?
Tip: When working with set theory, it's helpful to draw Venn diagrams to visualize operations like union and intersection.
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Math Problem Analysis
Mathematical Concepts
Set Theory
Union Operation
Intersection Operation
Formulas
Union: A ∪ B
Intersection: A ∩ B
Set Difference: A - B
Theorems
Set Union Identity
Intersection and Union Distribution
Suitable Grade Level
Grades 10-12
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