# 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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