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