Chapter 1, Problem 1TE

Write “the set of all natural numbers N less than 9” in two different ways.

To determine

To write: “The set of all natural numbers N less than 9” in two different ways.

Answer to Problem 1TE

“The set of all natural numbers N less than 9” can be written in two different ways as $A=\left\{1,2,3,4,5,6,7,8\right\}$ and $A=\left\{x|x<9,x\in N\right\}$.

Explanation of Solution

The set of all natural numbers is given by the infinite set $N=\left\{1,2,3,4,5,6,\cdots \right\}$.

Let A be the set of all natural numbers N less than 9.

Since A is a finite set, it can be written as, $A=\left\{1,2,3,4,5,6,7,8\right\}$.

Now, use the set builder form to represent the set A.

Let x be any natural number and N be the set of all natural numbers.

Then, A can be written as, $A=\left\{x|x<9,x\in N\right\}$.

Therefore, “the set of all natural numbers N less than 9” can be written in two different ways as $A=\left\{1,2,3,4,5,6,7,8\right\}$ and $A=\left\{x|x<9,x\in N\right\}$.