Exercise · ZW-SET-009 · ★★★ Advanced
If A = {∅}, then...
Choose one option.
Show answer
- A. ∅ ∈ A and ∅ ⊆ A
Explanation
A = {∅} has one element, which is ∅, so ∅ ∈ A. In addition, the empty set is contained in every set, so ∅ ⊆ A. Both hold at once, which is why A is not empty.
Review the concept: Set
A set is a well-defined collection of objects, called elements. Whether an object belongs to the set must be decidable without ambiguity.
\[x \in A \lor x \notin A\]
More practice problems: set
- ZW-SET-001 Which of the following best describes a set?
- ZW-SET-002 If x ∈ A, what does it mean?
- ZW-SET-003 If A = {1, 2, 3}, which statement is true?
- ZW-SET-004 Which symbol represents the empty set?
- ZW-SET-005 How many elements does A = {a, b} have?
- ZW-SET-006 If A = \1,2,3\, which statement is true?
- ZW-SET-007 Two sets are equal when...
- ZW-SET-008 Which statement is true?