Source : Webster's Revised Unabridged Dictionary (1913)

Conversely \Con"verse*ly\ (? or ?; 277), adv.
   In a converse manner; with change of order or relation;
   reciprocally. --J. S. Mill.

Source : WordNet®

conversely
     adv : with the terms of the relation reversed; "conversely, not
           all women are mothers"