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How to show a bijection between R^R and the power set of R

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I want to solve Q15 and also Q14. I have to show that these sets have the same cardinality by showing a bijection map from one set to another. For Q15 I have thought that the bijection map betweeen R^R and P(R) can be as follows : the functions which map from R to R represent the cardinality of R^R and such functions will have their domain and codomains in the power set of R, so we have a bijection. Is the approach correct in this case?

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