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

Full solution

Q. The number yy is rational. ee is the base of the natural logarithm. Which statement about yey - e is true?\newlineChoices:\newline(A) yey - e is rational.\newline(B) yey - e is irrational.\newline(C) yey - e can be rational or irrational, depending on the value of yy.
  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. Rational vs. Irrational: We know:\newlineyy is a rational number.\newlineee is an irrational number.\newlineWhich statement about yey - e is true?\newlineIf yy is a rational number and ee is an irrational number, then their difference yey - e is always an irrational number. This is because the difference between a rational and an irrational number is always irrational.
  3. True Statement: Therefore, the correct statement about yey - e is that yey - e is irrational.

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