The number $w$ is irrational. $e$ is the base of the natural logarithm. Which statement about $w - e$ is true? $\newline$ Choices: $\newline$ (A) $w - e$ is rational. $\newline$ (B) $w - e$ is irrational. $\newline$ (C) $w - e$ can be rational or irrational, depending on the value of $w$ .

Full solution

Q. The number

w

is irrational.

e

is the base of the natural logarithm. Which statement about

w - e

is true?

\newline

Choices:

\newline

(A)

w - e

is rational.

\newline

(B)

w - e

is irrational.

\newline

(C)

w - e

can be rational or irrational, depending on the value of

w

Identify Number Type: Identify whether $e$ is a rational or irrational number. $\newline$ The number $e$ (approximately $2.71828$ ) is known to be an irrational number.
Consider Properties: Consider the properties of irrational numbers. The difference between two irrational numbers can be either rational or irrational. It depends on the specific numbers involved.
Analyze Given Statements: Analyze the given statements with respect to the properties of irrational numbers. If $w$ is an irrational number and $e$ is also an irrational number, then $w - e$ could be rational if $w$ and $e$ are specifically related in such a way that their difference is a rational number. For example, if $w$ were some rational number plus $e$ , then $w - e$ would be that rational number. However, if $w$ is not specifically related to $e$ in this way, then $w - e$ would be irrational.
Determine True Statement: Determine which statement is true based on the analysis. $\newline$ Since $w - e$ can be rational or irrational depending on the specific value of $w$ , the correct statement is that $w - e$ can be rational or irrational, depending on the value of $w$ .