Exercise · ZW-COUNTABLE-SET-009 · ★★☆ Intermediate
Which statement about subsets of countable sets is correct?
Choose one option.
Show answer
- B. Every subset of a countable set is countable.
Explanation
A subset of a countable set is finite or equipotent to \(\mathbb{N}\), so it is countable. \(\mathbb{N}\) is an infinite subset of itself, infinite subsets of \(\mathbb{N}\) are countable rather than of the cardinality of \(\mathbb{R}\), and \(\mathbb{Q}\) contains \(\mathbb{N}\).
Review the concept: Countable set
A set is countable if it is finite or equipotent to \(\mathbb{N}\), that is, if its elements can be listed in a sequence.
\[A \text{ numerable} \iff A \text{ finito} \lor A\sim\mathbb{N}\]
More practice problems: countable set
- ZW-COUNTABLE-SET-001 What does it mean for a set A to be countable?
- ZW-COUNTABLE-SET-002 Which of these sets is countable?
- ZW-COUNTABLE-SET-003 What is a set equipotent to ℕ called?
- ZW-COUNTABLE-SET-004 What is an enumeration of a countably infinite set A?
- ZW-COUNTABLE-SET-005 Is a finite set countable?
- ZW-COUNTABLE-SET-006 Which of these functions is a bijection from ℕ onto ℤ?
- ZW-COUNTABLE-SET-007 Is ℕ×ℕ countable?
- ZW-COUNTABLE-SET-008 Is ℚ countable?