(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

You have a set A. Let [tex]B^{A}[/tex] be the set of all functions mapping A into the set B={0,1}. Prove the cardinality of[tex]B^{A}[/tex] = the cardinality of the power set of A.

2. Relevant equations[/b

3. The attempt at a solution

I feel about 50% sure about the proof. What do you think? Since A is a set, A has n elements where n is a natural number. Let g be the function mapping A into B s.t {n[tex]\in[/tex]A : n = 0 or n = 1}. So for each n in A there are 2 distinct possibilities (i. e mapping to 0 or 1). Since [tex]B^{A}[/tex] is the set containing all functions of type g, the cardinality of [tex]B^{A}[/tex] = [tex]2^{n}[/tex], which is also known as the cardinality of the power set of A.

Thanks for helping!

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# Homework Help: Help with proof

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