Math Problem Statement
(-3,5) U {-3-1,0,2,4,5,6,7,8,9}
Solution
The notation you’ve provided represents a union operation between two sets. Let’s break it down and simplify.
Step 1: Understanding the Sets
-
Set 1:
The interval is an open interval, which means it includes all real numbers between and , but does not include the endpoints and . -
Set 2:
This is a discrete set that consists of specific integer elements.
Step 2: Union of Sets
The union of these sets, , will include:
- All elements from the interval , which includes all real numbers from slightly greater than to slightly less than .
- All specific integers in Set 2.
Step 3: Putting It Together
Now we combine them into a single set that represents all unique elements within the union:
So, the union simplifies to:
This is your final representation of the union of these two sets.
Would you like further details or explanations on any step?
- What is the difference between open and closed intervals?
- How does union differ from intersection in set theory?
- Can we represent this union on a number line?
- How do we handle intervals when they overlap with discrete sets?
- What are some applications of union and intersection in real-world problems?
Tip: In set notation, always verify if intervals are open, closed, or half-open to ensure accuracy in representation.
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Math Problem Analysis
Mathematical Concepts
Set Theory
Union of Sets
Interval Notation
Formulas
Union of sets formula: A ∪ B
Theorems
Union of Sets
Properties of Intervals in Set Theory
Suitable Grade Level
Grades 9-11