Exercise · ZW-SUBSET-009 · ★★★ Advanced
Which statement is always true for any set A?
Choose one option.
Show answer
- D. A ⊆ A
Explanation
A ⊆ A is always true because every element of A is in A. A ∈ A does not hold in general (for example, if A = {1}), A ⊂ A proper is false because A equals itself, and {A} ⊆ A requires A ∈ A, so it does not hold in general either.
Review the concept: Subset
A set A is a subset of B when every element of A also belongs to B.
\[A \subseteq B \Longleftrightarrow \forall x\,(x\in A \Rightarrow x\in B)\]
More practice problems: subset
- ZW-SUBSET-001 If A = {1,2} and B = {1,2,3}, which relation is true?
- ZW-SUBSET-002 A ⊆ B means that...
- ZW-SUBSET-003 Which statement is false?
- ZW-SUBSET-004 For any set A, it always holds that...
- ZW-SUBSET-005 The empty set is a subset of...
- ZW-SUBSET-006 If A ⊆ B and B ⊆ C, what can be concluded?
- ZW-SUBSET-007 A ⊂ B usually indicates that...
- ZW-SUBSET-008 How many subsets does {a,b} have?