Exercise · ZW-SET-MEMBERSHIP-010 · ★★★ Advanced
Let \(A = \{\varnothing, \{\varnothing\}\}\). How many of the sets \(\varnothing\), \(\{\varnothing\}\) and \(\{\{\varnothing\}\}\) belong to A?
Choose one option.
Show answer
- D. 2
Explanation
\(\varnothing\) and \(\{\varnothing\}\) are elements of A, but \(\{\{\varnothing\}\}\) is not: it is a set different from both elements 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-007 Let A = \∅, \∅\\. Which statement is true?
- ZW-SET-MEMBERSHIP-008 Let B = \1, \1\, \\1\\\. How many elements does B have?