Exercise · ZW-SUBSET-006 · ★★☆ Intermediate
If A ⊆ B and B ⊆ C, what can be concluded?
Choose one option.
Show answer
- C. A ⊆ C
Explanation
Containment is transitive: if x ∈ A, then x ∈ B because A ⊆ B, and then x ∈ C because B ⊆ C. Therefore A ⊆ C. We cannot conclude C ⊆ A or A = C, and A ∈ C mixes membership with containment.
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-007 A ⊂ B usually indicates that...
- ZW-SUBSET-008 How many subsets does {a,b} have?
- ZW-SUBSET-009 Which statement is always true for any set A?