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

Question

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

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Identify Number Type: Identify whether e is a rational or irrational number. 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. 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.

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 $w$ .

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