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1. Recall that P(X) = {S | SC X} and define, for any sets X and Y, Scart (X, Y) = {X₁ x Y₁ | X₁ CX and Y₁ CY₂}. Suppose |A| = 5 and |B| = 8. Calculate the following cardinalities (show your work): 2 (a) P (P(A)) x P (P(B))| (b) P (P(A) x P(B))| (c) Scart (P(A), P(B))| Find the following cardinalition (Do list the olemont. ota) (Notationi

1. Recall that P(X) = {S | SC X} and define, for any sets X and Y, Scart (X, Y) = {X₁ x Y₁ | X₁ CX and Y₁ CY₂}. Suppose |A| = 5 and |B| = 8. Calculate the following cardinalities (show your work): 2 (a) P (P(A)) x P (P(B))| (b) P (P(A) x P(B))| (c) Scart (P(A), P(B))| Find the following cardinalition (Do list the olemont. ota) (Notationi

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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1. Recall that P(X) = {S SC X} and define, for any sets X and Y, Scart (X,Y)= {X₁ x Y₁ | X₁ CX and Y₁ CY₂}. Suppose |A| = 5 and |B| = 8. Calculate the following cardinalities (show your work): (a) P (P(A)) x P (P(B))| (b) P (P(A) x P(B))| (c) Scart (P(A), P(B))| 2. Find the following cardinalities (Do not list the elements of the sets). (Notation:
Transcribed Image Text:1. Recall that P(X) = {S SC X} and define, for any sets X and Y, Scart (X,Y)= {X₁ x Y₁ | X₁ CX and Y₁ CY₂}. Suppose |A| = 5 and |B| = 8. Calculate the following cardinalities (show your work): (a) P (P(A)) x P (P(B))| (b) P (P(A) x P(B))| (c) Scart (P(A), P(B))| 2. Find the following cardinalities (Do not list the elements of the sets). (Notation:
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