For a real number r, define Sr to be the interval [r-1, r+2]. Let A={1,3,4}. Determine ⋃α∈A Sαan

Step 1: Identify the intervals u005C( S_u005Calpha u005C) for each u005C(u005Calpha u005Cin Au005C).u000Au000Au002D For u005C(u005Calpha u003D 1u005C),

For a real number r, define Sr to be the interval [r-1,...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Real Intervals

Real intervals are contiguous subsets of the real number line defined by their endpoints. Intervals can be open, closed, or half-open, and they provide a structured way to represent subsets of real numbers, often used in analysis and calculus.

Translation of Intervals

Translation of intervals involves shifting an interval along the real number line by adding or subtracting a constant to each of its endpoints. This concept helps in understanding how intervals change position without altering their length or structure, and it is useful when intervals depend parametrically on a variable.

Set Union

Set union is an operation that takes a collection of sets and forms a new set containing all elements that are in any of the sets. This concept is fundamental in set theory and is used to combine multiple sets into one comprehensive set.

Set Intersection

Set intersection is an operation that takes a collection of sets and forms a new set consisting of only those elements that are common to every set in the collection. This concept is essential in various areas of mathematics for identifying shared elements across different sets.

For a real number $r$, define $S_r$ to be the interval $[r-1, r+2]$. Let $A=\{1,3,4\}$. Determine $\bigcup_{\alpha \in A} S_\alpha$ and $\bigcap_{\alpha \in A} S_\alpha$.

Instant Answer

Please give Ace some feedback