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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
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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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.
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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