Exercise · ZW-POWER-SET-010 · ★★☆ Intermediate
Let \(|A|=2\). How many subsets does \(\mathcal{P}(A)\) have?
Choose one option.
Show answer
- D. 16
Explanation
\(\mathcal{P}(A)\) has \(2^2=4\) elements, so it has \(2^4=16\) subsets. The value 4 is the number of elements of the power set, not the number of its subsets.
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-003 How many elements does P(\1,2,3\) 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?