Math Problem Statement
Let U = set of all real numbers, P ={x|-5< or equal to x < 10}, Q={x|4<x<20}, and R={x|x, or equal to 6}: write in interval notation: PUQ
Solution
Let's break this down:
-
is the set of real numbers from to , including but excluding .
- In interval notation: .
-
is the set of real numbers from to , excluding both endpoints.
- In interval notation: .
Now, we want to find , the union of sets and .
- The union of two sets includes all elements that are in either set.
- Looking at the intervals:
When combining these intervals, we consider the overlap and non-overlap:
- From to is covered by , and from to is covered by .
- The interval from to is shared, but we need to combine all elements from to (with the exception of the gap at , which is excluded from but included in ).
Thus, is:
This includes all real numbers from to , with included and excluded.
Would you like more details or have any other questions?
Here are 5 related questions you might find helpful:
- What does the intersection of two sets mean, and how would we calculate it for and ?
- How does the union of intervals work in real-world scenarios?
- Can the union of two sets have gaps, or do they always form continuous intervals?
- How does the concept of a set relate to the number line in mathematics?
- What is the difference between inclusive and exclusive boundaries in interval notation?
Tip: Always pay attention to whether the endpoints are included or excluded (denoted by square brackets or parentheses ) when working with intervals!
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Math Problem Analysis
Mathematical Concepts
Set Theory
Interval Notation
Union of Sets
Formulas
P = [-5, 10)
Q = (4, 20)
P ∪ Q = [-5, 20)
Theorems
Union of Sets
Interval Union
Suitable Grade Level
Grades 9-11