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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) | 4 Million Minutes Watch Time | 8+ Years Experience | Youtube: Maths Wallah | vineetloomba.com

U
Unacademy user
I just loved the way u teach.... it's really good
Siva Prasad
a year ago
Glad to know that Vandana :)
CR
Statement pattern and Logical Equivalence Quantifiers and Quantified Statements Algebra of statements(Standard equivalent statements)(laws) Application of logic to switching circuits Ye Maharashtra board ke kuch topics hai iss chapter ke... It's my request plz upload them sir.🤗
CR
Sir saare laws aur Switching circuit ke videos bhi upload kijiye plzzzz
Vineet Loomba
24 days ago
Kis exam k syllabus me h ye
sir APPLICATIONS TO SWITCHING CIRCUIT AND ALGEBRA BHI KARWA DIJIYE
Vineet Loomba
a month ago
This is not in syllabus
Om Kendre
a month ago
ok
sir "and"&"or" connectives Kon Kon si property hold krte h? do they hold "associative property" ?
sir MAHARASHTRA board mein 4 mmark question ate hai construct truth table wale woh kardijeye
  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)