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

  1. Set 1: (3,5)(-3, 5)
    The interval (3,5)(-3, 5) is an open interval, which means it includes all real numbers between 3-3 and 55, but does not include the endpoints 3-3 and 55.

  2. Set 2: {4,1,0,2,4,5,6,7,8,9}\{-4, -1, 0, 2, 4, 5, 6, 7, 8, 9\}
    This is a discrete set that consists of specific integer elements.

Step 2: Union of Sets

The union of these sets, (3,5){4,1,0,2,4,5,6,7,8,9}(-3, 5) \cup \{-4, -1, 0, 2, 4, 5, 6, 7, 8, 9\}, will include:

  • All elements from the interval (3,5)(-3, 5), which includes all real numbers from slightly greater than 3-3 to slightly less than 55.
  • 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:

(3,5){4,1,0,2,4,5,6,7,8,9}=(3,5){5,6,7,8,9}(-3, 5) \cup \{-4, -1, 0, 2, 4, 5, 6, 7, 8, 9\} = (-3, 5) \cup \{5, 6, 7, 8, 9\}

So, the union simplifies to:

(3,5){5,6,7,8,9}(-3, 5) \cup \{5, 6, 7, 8, 9\}

This is your final representation of the union of these two sets.

Would you like further details or explanations on any step?


  1. What is the difference between open and closed intervals?
  2. How does union differ from intersection in set theory?
  3. Can we represent this union on a number line?
  4. How do we handle intervals when they overlap with discrete sets?
  5. 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