Chapter 1.2, Problem 3P

To determine

a.

To write:

The given set in roster form

Solution:

$\{6, 7, 8, 9\}$

Explanation:

Concept:

A set is a collection of objects. The objects of a set are called its members or elements. When the elements of a set are listed, the set is said to be written in roster form.

Calculation:

$\left\{x\right|x \mathrm{i}\mathrm{s}\mathrm{ }\mathrm{a}\mathrm{ }\mathrm{w}\mathrm{h}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{ }\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{ }\mathrm{b}\mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n}\mathrm{ }5\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }10\}$

The set contains the element $x$ such that $x$ is a whole number between $5$ and $10$.

Therefore, the set can be written in roster form as

$\{6, 7, 8, 9\}$

Final statement:

The given set in roster form is $\{6, 7, 8, 9\}$.

b.

To write:

The given set in roster form

Solution:

$\{41, 42, 43, 44, \dots \dots \dots ..\}$

Explanation:

Calculation:

$\left\{x\right|x \mathrm{i}\mathrm{s}\mathrm{ }\mathrm{a}\mathrm{ }\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{ }\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{ }\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{ }\mathrm{t}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{ }40\}$

The set contains the element $x$ such that $x$ is a natural number greater than $\mathrm{ }40$.

Therefore, the set can be written in roster form as

$\{41, 42, 43, 44, \dots \dots \dots ..\}$

Final statement:

The given set in roster form is $\{41, 42, 43, 44, \dots \dots \dots ..\}$.