12.3.4 Duality
Chapter 9: Chapter 12 · MATHEMATICS-VOLUME 2 · EN medium
From your actual textbook ✓
What does your textbook say about 12.3.4 Duality?
. . 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 .
📖 Class 12 Mathematics English Volume 2 2025 Edition www.tntextbooks.in · Page 247
Read from the source
Complete lesson
. . 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 ].
Related topics
Want this shaped for your exam marks?
Get an AI answer grounded in your actual textbook — with the exact page reference.
Ask AI about this topic →