For any set A, finite or infinite, let B^A be the set of all functions mapping A into the set B

Name: For any set A, finite or infinite, let B^A be the set of all functions mapping A into the set B = 0, 1. Show that the cardinality of B^A is the same as the cardinality of the set P(A). [Hint: Each element of B^A determines a subset of A in a natural way.]
Uploaded: 2022-09-29T11:03:41-08:00
Duration: 2 min 15 s
Channel: Madhur L
Description: For any set A, finite or infinite, let B^A be the set of all functions mapping A into the set B = 0, 1. Show that the cardinality of B^A is the same as the cardinality of the set P(A). [Hint: Each element of B^A determines a subset of A in a natural way.]

Question

Suman K · Accepted Answer

First, we need to understand what the set B^A represents. It is the set of all functions from A

Question

For any set A, finite or infinite, let B^A be the set of all functions mapping A into the set B = {0, 1}. Show that the cardinality of B^A is the same as the cardinality of the set P(A). [Hint: Each element of B^A determines a subset of A in a natural way.]

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