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The number uu is rational. ee is the base of the natural logarithm. Which statement about u+eu + e is true?\newlineChoices:\newline(A) u+eu + e is rational.\newline(B) u+eu + e is irrational.\newline(C) u+eu + e can be rational or irrational, depending on the value of uu.

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Q. The number uu is rational. ee is the base of the natural logarithm. Which statement about u+eu + e is true?\newlineChoices:\newline(A) u+eu + e is rational.\newline(B) u+eu + e is irrational.\newline(C) u+eu + e can be rational or irrational, depending on the value of uu.
  1. Identify Number Type: Identify whether ee is a rational or irrational number.ee is the base of the natural logarithm and is known to be an irrational number.
  2. Given Information: We know:\newlineuu is a rational number.\newlineee is an irrational number.\newlineConsider the nature of the sum u+eu + e.\newlineThe sum of a rational number and an irrational number is always irrational.
  3. Consider Sum Nature: Therefore, no matter what rational value uu has, the sum u+eu + e will always be irrational.\newlineThis is because the irrational part (ee) cannot be expressed as a ratio of two integers, and adding a rational number to it does not change this fact.

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