Often in binary classification we are interested in the differences in the output of our current

classifier, g$,$ and an unknown function f that we are trying to learn. It is common in these

cases to examine the quantity produced by f$($x$)$g$($x$)$ for a given input x$.$ For this problem,

let D be an arbitrary distributio n on the domain $\{1,1\}$n$,$ and let f$,$ g : $\{1,1\}$n $->\{1,1\}$

be two Boolean functions. Would this still be true if the domain were some other domain $($such as

Rn$,$ where R denotes the real numbers, with say the Gaussian distribution$)$ instead of

$\{1,1\}$n$?$ If yes, justify your answer. If not, give a counterexample.

Note: Only the domain changes here. The output is still boolean.