Help on proving equal cardinalities

Hello, I am trying to proof the following claim.

Where is the power set and .

I am trying to construct a bijection or two injections and cantors theorem to proof they have the same cardinality, but I seem to be getting nowhere. Can anyone help me?

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Re: Help on proving equal cardinalities

Re: Help on proving equal cardinalities

So the in the red line from picture would be the resulting set by the function for a particular and

Re: Help on proving equal cardinalities

Quote:

Originally Posted by

**gordo151091** So the

in the red line from picture would be the resulting set by the function

for a particular

and

Yes. The blobby area in the picture is supposed to represent a subset S of AxB, and is the function whose value at a point is the set of second coordinates of all points in S whose first coordinate is