Problem 17.5. Consider the function ?(0,1) : R ? R (this is thecharacteristic of Definition 14.4). Find: (a) ?(0,1)((0,1)); (b)?(0,1)((?1,3)); (c) and (in general) ?(0,1)((a,b)), where a,b ? Rand a < b; prove that the set you found is correct; (d) ??1(0,1) ((?2,?1)); (e) ??1 (0,1) ((0,2)); (f) and (in general) ??1(0,1) ((a,b)), where a,b ? R and a < b; prove that the set youfound is correct,
Definition 14.4 (for Problems 14.6 through 14.9). Let X be anonempty set and let
A be a subset of X. The characteristic function or indicatorfunction of the set A
in X is
?A : X ? {0,1} defined by ?A(x) = 1 if x ? A
0 if x ? XA
