Math Problem Statement
Solution
The sets and are defined as:
We are tasked with finding (union of and ) and (intersection of and ) using interval notation.
1. (Union):
The union of two sets includes all elements that are in either set. Since and , the union will cover all values starting from (the lower bound of ) and going to infinity. Hence, the union is:
2. (Intersection):
The intersection of two sets includes only the elements that are common to both sets. Since includes all values greater than or equal to 4, and includes all values greater than 9, their intersection will be all values greater than 9. Hence, the intersection is:
Final Answer:
Would you like more details or further clarifications?
Here are five follow-up questions:
- What is the difference between open and closed intervals?
- How do we determine the union and intersection when sets are defined with inequalities?
- What happens if two sets have no common elements?
- How do unions and intersections apply to more than two sets?
- How do we handle cases where the sets are defined on finite intervals?
Tip: In set theory, always pay attention to whether the boundaries are included (closed intervals) or not (open intervals), as this changes the result significantly.
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Math Problem Analysis
Mathematical Concepts
Set Theory
Union of Sets
Intersection of Sets
Interval Notation
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12
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