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Tautology | Fallacy (Contradiction) | Duality (in Hindi)
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This lesson discusses the concepts of tautology, fallacy and Duality in detail

Vineet Loomba is teaching live on Unacademy Plus

Vineet Loomba
IITian | No. 1 Educator in IIT-JEE (Maths) | 2.6 Million Minutes Watch Time | 8+ Years Experience | Youtube: Maths Wallah | vineetloomba.com

Unacademy user
converse topic sir please add
Duality+Tautology+Contradictory = (Question with most amount of silly mistakes) which I am making after a month of revising Mathematical Reasoning! Here sir you explained the concept brilliantly! Really amazing!
Vineet Loomba
6 months ago
Thanks ..dont forget to rate the course 5 stars .
Sir properties wali table! add that! beneficial thing for the course enhancement!
Vineet Loomba
6 months ago
Okay sure
sirr... plz add some questions...
  1. MATHEMATICAL REASONING ALL YoU NEED FOR JEE MAIN (NTA SPECIAL) JEE MAIN RANK BOOSTER COURSE PREPARED BY ER. VINEET LOOMBA ITIAN IIT-JEE MENTOR


  2. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B. Tech. From IIT Roorkee IIT-JEE Mentor Since 2010. * Many of my students are pursuing courses in IITs, NITs, BITs etc unacademy Currently running my own Coaching Institute for JEE Main and Advanced Follow me @ https://unacademy.com/user/vineetloomba to get updates or search me on Google


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  5. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Tautology: This is a statement which always true for all truth values of its components. Consider p v p Truth tabl e Last columns is always true. Hence p v ~ p is a tautology. SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEE)


  6. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex.Prove by construction of truth table that pv ~(p q) is a tautology. Sol.Truth table TTIT TFF FITI F Since the last column shows T's only, therefore p v ~ (p A q) is a tautology. SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEE)


  7. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Fallacy (contradiction) : This is statement which is always false for all truth values of its components Ex. A-p Last columns is always false. Hence p ~ p is a fallacy (contradiction). SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEE)


  8. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex.Prove by constructing truth table that (p Aq)A~(p v q) is a fallacy (contradiction) Sol. Truth table Since the last column shows F's only, therefore (p ^ q) ~ (pv q) is a fallacy. SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEE)


  9. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Duality The compound statements si and s2 are said to be duals of each other if one can be obtained from the other by replacing by v and v by . The connectives and are also called duals of each other. Ex.Write the duals of the following statements (ii) (pv q) ^ (r/ s) Sol. The required duals are given by (ii) ( q) (r ^ s) SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)


  10. 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) If the compound statements s contains the special variables t(tautology) or c (contradiction), then dual of s is obtained by replacing t by c and c by t and ^ by v and v and as usual. Ex.Write the dual of the following statements: (i) (p v q) A C (iii) (p ^ q) v t (ii) (p v t)/\ r (iv) (pv q) v C Sol. The required duals are given by: (i) (p ^ q) t (iii) (pv q) ^ c (ii) (p A c) vr (iv) (p q) ^ t SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)