Exercise · ZW-POWER-SET-007 · ★★☆ Intermediate
What is \(\mathcal{P}(\{a\}) \cap \{a\}\)?
Choose one option.
Show answer
- C. \(\varnothing\)
Explanation
The elements of \(\mathcal{P}(\{a\})\) are \(\varnothing\) and \(\{a\}\), and neither of them is \(a\). Since \(\{a\}\) has only the element \(a\), the intersection is empty.
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-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?