Exercise · ZW-SUBSET-008 · ★★☆ Intermediate
How many subsets does {a,b} have?
Choose one option.
Show answer
- A. 4
Explanation
{a, b} has 4 subsets: ∅, {a}, {b} and {a, b}. In general a set with n elements has 2ⁿ subsets; here 2² = 4.
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?
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- 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-009 Which statement is always true for any set A?