Chapter R.1, Problem 1E

To determine

To identify:

The set $\left\{4, 5, 6, \dots , 15\right\}$ as finite or infinite and find whether $10$ is an element of the set.

Answer to Problem 1E

Solution:

The given set $\left\{4, 5, 6, \dots , 15\right\}$ is finite and $10 \in \left\{4, 5, 6, \dots , 15\right\}$.

Explanation of Solution

Concept:

A finite set is one that has a limited number of elements. The process of counting its elements comes to an end.

A set that has an unending list of distinct elements is called an infinite set.

Calculation:

The given set $\left\{4, 5, 6, \dots , 15\right\}$ is finite since the process of counting the elements $4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14$ and $15$ comes to an end.

The number $10$ belongs to the set and can be written as

$10 \in \left\{4, 5, 6, \dots , 15\right\}$

Final statement:

The given set $\left\{4, 5, 6, \dots , 15\right\}$ is finite and $10 \in \left\{4, 5, 6, \dots , 15\right\}$.