# Math Help - conditional entropy of function

1. ## conditional entropy of function

how does one show that H(Y l f(X) ) greater than or equal to H(YlX) where f(X) is any function of X?

2. ## Re: conditional entropy of function

$f(X)$ is a degraded observation of $X$, so we have that

$H(Y|f(X),X) = H(Y|X)$

Since conditioning reduces entropy,

$H(Y|f(X)) \geq H(Y|X)$