Exercise · ZW-SET-MEMBERSHIP-007 · ★★☆ Intermediate
Let \(A = \{\varnothing, \{\varnothing\}\}\). Which statement is true?
Choose one option.
Show answer
- C. \(\varnothing \in A\) and \(\{\varnothing\} \in A\)
Explanation
Both objects are elements of A. The other options claim that \(\varnothing \notin A\), which is false because \(\varnothing\) is an element of A.
Review the concept: Set membership
The relation stating that an object \(x\) is one of the elements of a set \(A\), symbolized by \(\in\).
\[x \in A\]
More practice problems: set membership
- ZW-SET-MEMBERSHIP-001 What does x ∈ A mean?
- ZW-SET-MEMBERSHIP-002 What is the negation of x ∈ A?
- ZW-SET-MEMBERSHIP-003 Let A = \1, 2, 3\. Which statement is true?
- ZW-SET-MEMBERSHIP-004 Let A = \∅, \1\\. Which statement is true?
- ZW-SET-MEMBERSHIP-005 Can a set contain the same element twice?
- ZW-SET-MEMBERSHIP-006 Which symbol expresses that x does not belong to A?
- ZW-SET-MEMBERSHIP-008 Let B = \1, \1\, \\1\\\. How many elements does B have?
- ZW-SET-MEMBERSHIP-009 Let C = \\1\, \2\, \3\\. Which statement is true?