Exercise · ZW-SUBSET-010 · ★★★ Advanced
If 1 ∈ A, which statement does not necessarily follow?
Choose one option.
Show answer
- C. {1} ∈ A
Explanation
If 1 ∈ A, then {1} ⊆ A and A is not empty. But {1} ∈ A says something different: that the set {1} is an element of A, and that does not follow. Example: A = {1, 2}: {1} ⊆ A, but {1} ∉ A.
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
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- ZW-SUBSET-008 How many subsets does {a,b} have?