Wednesday, 2 January 2013

functions - Prove Cardinality of Sets Exponentiation

I am studying for an exam in elementary set theory and I am not understanding the proof for this theorem:



For any three sets $A,B,C$:



$(A^B)^C \sim A^{(B \times C)}$



I know I need to find a bijective function $G : (C\rightarrow A^B) \rightarrow (B\times C \rightarrow A)$.
But I don't have a clue.




Any help would be appreciated.
Thanks

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