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Conditional entropy H(X|Y) is bounded by $0 \le H$(X|Y) ≤ $H(X)$ because learning the value of Y provides information that can only reduce or leave unchanged the average uncertainty about X; it cannot increase it on average.

Conditions: X and Y are discrete random variables.

Conditional entropy H(X|Y) is bounded by $0 \le H$(X|Y) ≤ $H(X)$ because learning the value of Y provides information that can only reduce or leave unchanged the average uncertainty about X; it cannot increase it on average.

Conditions: X and Y are discrete random variables.