Infinities are weird

Suppose axiom of choice is true. Let \(A\) be an uncountable set and \(B\) be a countable set. Which of these statements relate \(|A|\) to \(|A \setminus B|\)?

  • A. \(|A| < |A \setminus B|\), always.
  • B. \(|A| = |A \setminus B|\), always.
  • C. \(|A| > |A \setminus B|\), always.
  • D. \(|A| \le |A \setminus B|\); both smaller than and equality cases can occur.
  • E. \(|A| \neq |A \setminus B|\); both smaller than and greater than cases can occur.
  • F. \(|A| \ge |A \setminus B|\); both greater than and equality cases can occur.
  • G. None of the above choices
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