. . Duality Definition . The dual of a statement formula is obtained by replacing ∨ by ∧∧ , ∧∧ by ∨ , T by F F by T .
A dual is obtained by replacing 𝕋 (tautology) by 𝔽 (contradiction) , and, 𝔽 by 𝕋 . Remarks ( ) The symbol ¬ is not changed while finding the dual. ( ) Dual of a dual is the statement itself. ( ) The special statements 𝕋 (tautology) and 𝔽 (contradiction) are duals of each other.
( ) T is changed to F and vice-versa. - - Principle of Duality If a compound statement S contains only ¬ , ∧ , and ∨ and statement S arises from S by replacing ∧ by ∨ , and, ∨ by ∧ then S is a tautology if and only if S is a contradiction. For example (i) The dual of ( s ∨ 𝔽 is ( s ∧ 𝕋 . (ii) The dual of p ∧ [ ¬ q ¬ r ] is p ∨ [ ¬ q ¬ r ].