Given A = {3, 6, 9, 10, 12} and B = {1, 6, 9, 12}, find each of the following set cardinalities: n(P(A) N P(B)) = n(P(A) x P(B)) = n(P(A) U P(B)) = n(P(AU B)) =
Given A = {3, 6, 9, 10, 12} and B = {1, 6, 9, 12}, find each of the following set cardinalities: n(P(A) N P(B)) = n(P(A) x P(B)) = n(P(A) U P(B)) = n(P(AU B)) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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discrete math
![Given \( A = \{3, 6, 9, 10, 12\} \) and \( B = \{1, 6, 9, 12\} \), find each of the following set cardinalities:
\[ n(\mathcal{P}(A) \cap \mathcal{P}(B)) = \] \(\square\)
\[ n(\mathcal{P}(A) \times \mathcal{P}(B)) = \] \(\square\)
\[ n(\mathcal{P}(A) \cup \mathcal{P}(B)) = \] \(\square\)
\[ n(\mathcal{P}(A \cup B)) = \] \(\square\)
In the context of these problems:
- \(\mathcal{P}(A)\) represents the power set of \(A\), which is the set of all subsets of \(A\).
- \(\mathcal{P}(B)\) is the power set of \(B\), consisting of all subsets of \(B\).
- Cardinality refers to the number of elements in a set.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23afe9e0-d558-4f29-a475-77c743e5301e%2F43e98703-507e-49b8-bdae-abbc0bd30f4b%2F6vcnn3u_processed.png&w=3840&q=75)
Transcribed Image Text:Given \( A = \{3, 6, 9, 10, 12\} \) and \( B = \{1, 6, 9, 12\} \), find each of the following set cardinalities:
\[ n(\mathcal{P}(A) \cap \mathcal{P}(B)) = \] \(\square\)
\[ n(\mathcal{P}(A) \times \mathcal{P}(B)) = \] \(\square\)
\[ n(\mathcal{P}(A) \cup \mathcal{P}(B)) = \] \(\square\)
\[ n(\mathcal{P}(A \cup B)) = \] \(\square\)
In the context of these problems:
- \(\mathcal{P}(A)\) represents the power set of \(A\), which is the set of all subsets of \(A\).
- \(\mathcal{P}(B)\) is the power set of \(B\), consisting of all subsets of \(B\).
- Cardinality refers to the number of elements in a set.
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