Exercise · ZW-SET-008 · ★★☆ Intermediate
Which statement is true?
Choose one option.
Show answer
- B. ∅ ∈ {∅}
Explanation
{∅} is the set whose only element is ∅, so ∅ ∈ {∅} is true. But ∅ ≠ {∅}: one has no elements and the other has one. And ∅ ∈ ∅ is false because the empty set has no elements.
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-009 If A = {∅}, then...