Exercise · ZW-POWER-SET-003 · ★★☆ Intermediate
How many elements does \(\mathcal{P}(\{1,2,3\})\) have?
Choose one option.
Show answer
- C. 8
Explanation
Each of the 3 elements is either included or excluded, so there are \(2^3=8\) subsets. The value 6 forgets the empty set and \(\{1,2,3\}\) itself.
Review the concept: Power set
The set of all subsets of a set \(A\), denoted \(\mathcal{P}(A)\).
\[\mathcal{P}(A) = \{X : X \subseteq A\}\]
More practice problems: power set
- ZW-POWER-SET-001 What is P(A)?
- ZW-POWER-SET-002 How many elements does P(∅) have?
- ZW-POWER-SET-004 If X ∈ P(A), what holds?
- ZW-POWER-SET-005 Is ∅ ∈ P(A) for every set A?
- ZW-POWER-SET-006 Let A=\1,2,3,4\. How many elements of P(A) have exactly two elements?
- ZW-POWER-SET-007 What is P(\a\) ∩ \a\?
- ZW-POWER-SET-008 Which statement is true for every set A?
- ZW-POWER-SET-009 Let A=\a,b\. How many pairs (X,Y) with X,Y ∈ P(A) satisfy X ⊆ Y?