Chapter 8.6, Problem 54E

To determine

Whether the given statement is always, sometimes or never true.

Answer to Problem 54E

The given statement is always true.

Explanation of Solution

Given:

The given statement is:

An irrational number is a real number.

Calculation:

A rational number can be expressed as a ratio such as $\frac{p}{q}$ , where p and q are integers and q is not equal to 0.

For example:

  $\{-\frac{3}{2},-\frac{4}{3},\frac{1}{4},\frac{0}{1},\frac{2}{13},\mathrm{....}\}$

Therefore, an integer is always a rational number.

Also, any real number that is not a rational number is an irrational number.

Definition of real number states that all numbers that are rational, irrational or integers are real numbers.

Therefore, an irrational number is always a real number.

The given statement is always true.