Properties of sets

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Problem: Let the set \( A \subset \mathbb{R} \) is open, and \( B \subset \mathbb{R} \) is closed. Prove that the set \( A \backslash B \) is open, and \( B \backslash A \) is closed.

19.7.3 Properties of sets

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Problem: Prove that the set of rational numbers \( \mathbb{Q} \) is countable.

19.7.10 Properties of sets

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Problem: Using the theorem of nested intervals, prove that the segment is uncountable.

19.7.11 Properties of sets

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