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

Full solution

Q. is the base of the natural logarithm. The number vv is irrational. Which statement about v- v is true?\newlineChoices:\newline(A) v- v is rational.\newline(B) v- v is irrational.\newline(C) v- v can be rational or irrational, depending on the value of vv.
  1. Identify ee nature: Identify the nature of the number ee. The base of the natural logarithm, ee, is known to be an irrational number.
  2. Consider vv nature: Consider the nature of the number vv. The problem states that vv is an irrational number.
  3. Analyze eve - v: Analyze the expression eve - v.\newlineSince both ee and vv are irrational, the difference between two irrational numbers can be either rational or irrational. It depends on the specific values of ee and vv.\newlineFor example, if vv were equal to ee, then eve - v would be 00, which is rational.\newlineHowever, if vv were some other irrational number not related to ee in a way that their difference produces a rational number, then eve - v would remain irrational.
  4. Determine correct choice: Determine the correct choice based on the analysis.\newlineSince eve - v can be rational or irrational depending on the specific value of vv, the correct statement is that eve - v can be rational or irrational, depending on the value of vv.

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