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

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Q. The number qq is irrational. ee is the base of the natural logarithm. Which statement about q−eq - e is true?\newlineChoices:\newline(A) q−eq - e is rational.\newline(B) q−eq - e is irrational.\newline(C) q−eq - e can be rational or irrational, depending on the value of qq.
  1. Identify Type of Number: 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. Properties of Irrational Numbers: Consider the properties of irrational numbers. The difference between two irrational numbers can be rational or irrational. It depends on the specific numbers involved.
  3. Analyze Possible Outcomes: Analyze the possible outcomes for q−eq - e. If qq is specifically chosen to be equal to ee, then q−e=e−e=0q - e = e - e = 0, which is rational. If qq is any irrational number not specifically related to ee, then q−eq - e is likely to be irrational, but without knowing the exact value of qq, we cannot be certain.
  4. Conclude Statement: Conclude the statement about q−eq - e. Since q−eq - e can be rational (if q=eq = e) or irrational (if qq is not specifically related to ee), the correct statement is that q−eq - e can be rational or irrational, depending on the value of qq.

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