2. If X is any set, then the power set of X is P(X) = {A: A C X}, the set consisting of all subsets of X. E.g., P({a,b}) = {{a,b}, {a}, {b},Ø}. Let X be a nonempty set and suppose that f: X → P(X) is a function. (Then f(x) is a subset of X for every x E X). Set A = {x € X : x ¢ f(x)}. Show that A is not in the range of f. Remark. This shows that there is no surjection f: X – P(X).

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.