Determine if the set $\{5,2,4,1,3\}$ is a partition of $[1,5]$.

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Lesson Parent: 
Integration II: Partitioning the x-axis.
Problem: 

Determine if the set $\{5,2,4,1,3\}$ is a partition of $[1,5]$.

Answer: 

The set $\{5,2,4,1,3\}$ is a partition of $[1,5]$.

SAMPLE SOLUTION

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Solution: 

Recall that a partition of $[a,b]$ has the following properties:

  1. It includes the numbers $a$ and $b$.
  2. The other elements of the partition are between $a$ and $b$.

We typically write the partition such that <Sign in to see all the formulas>. If we do then both properties are automatically satisfied.

In this problem $a=1$ and $b=5$. Let's go through the properties:

  • The set does include $1$ and $5$.
  • The other elements of the set are $2$, $3$, and $4$ and are all between $1$ and $5$ so that property 2 is satisfied.

Therefore, the set <Sign in to see all the formulas> is a partition of $[1,5]$. However, we would typically write it as <Sign in to see all the formulas>.