"Suman is brilliant and dishonest" an be expressed as : P∧∼R So "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as : (P∧∼R)↔Q Now negation of this =∼[(P∧∼R)↔Q] You should know, p↔q≡q↔p So, ∼[(P∧∼R)↔Q]≡∼[Q↔(P∧∼R)]