Chapter A.11, Problem 1AYU

To determine

The integers and the rational numbers in the set $\left\{-3,\text{ 0, }\sqrt{2},\frac{6}{5},\pi \right\}$.

Answer to Problem 1AYU

The integers in the set $\left\{-3,\text{ 0, }\sqrt{2},\frac{6}{5},\pi \right\}$ is $\underset{\_}{\left\{-3,\text{ 0}\right\}}$.

The rational numbers in the set $\left\{-3,\text{ 0, }\sqrt{2},\frac{6}{5},\pi \right\}$ is $\underset{\_}{\left\{-3,\text{ 0, }\frac{6}{5}\right\}}$.

Explanation of Solution

It is given that, the set $\left\{-3,\text{ 0, }\sqrt{2},\frac{6}{5},\pi \right\}$.

Note that, the set of integers contains the numbers in the set $\left\{\mathrm{...},-3,-2\text{, }-1,0,1,\text{ 2, 3,}\mathrm{...}\right\}$ and a rational number is a number that can be expressed as a quotient $\frac{a}{b}$ of two integers, where the integer b cannot be 0.

It can be concluded that, the integers in the set $\left\{-3,\text{ 0, }\sqrt{2},\frac{6}{5},\pi \right\}$ is $\underset{\_}{\left\{-3,\text{ 0}\right\}}$ and the rational numbers in the set $\left\{-3,\text{ 0, }\sqrt{2},\frac{6}{5},\pi \right\}$ is $\underset{\_}{\left\{-3,\text{ 0, }\frac{6}{5}\right\}}$.