Exercise · ZW-POWER-SET-006 · ★★☆ Intermediate
Let \(A=\{1,2,3,4\}\). How many elements of \(\mathcal{P}(A)\) have exactly two elements?
Choose one option.
Show answer
- D. 6
Explanation
There are \(\binom{4}{2}=6\) ways to choose 2 of the 4 elements. The value 16 is the total number of subsets of \(A\), and 8 counts the subsets containing a fixed element.
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-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?