I choose D because :

a<b => a-b<0 which means a-b is negative so I is true.

0<a<b => ab>0 => \(\dfrac{1}{ab}\) is positive so II is true.

\(\dfrac{1}{b}\) -\(\dfrac{1}{a}\)=\(\dfrac{a-b}{ab}\) but a-b<0 and ab>0 => \(\dfrac{a-b}{ab}\) is negative so III is false