## Vineet Loomba is teaching live on Unacademy Plus

MATHEMATICAL REASONING ALL YoU NEED FOR JEE MAIN (NTA SPECIAL) JEE MAIN RANK BOOSTER COURSE PREPARED BY ER. VINEET LOOMBA ITIAN IIT-JEE MENTOR

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

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Follow me on Unacademy for Next live Special Class Strategy for JEE Main and Advanced V Limits, Continuity, Differentiability v Sets, Relations and Functions V Indefinite Integration V Definite Integratiorn Trigonometry VApplications of Derivatives Complex Number Permutations Combinations Binomial Theorem V Logarithmic Functions V Sequences Series V Straight Lines Applications of Integrals Circles (Detailed Course) Probability Most Important Questions in IIT-JEE Mathematics Parabola (Detailed Course) Ellipse (Detailed Course) Inverse Trigonometry Upcoming Courses next month: Coordinate Geometry Differential Equations

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) SPECIAL ANNOUNCEMENT Share useful links and advice with your learners... CRASH COURSE FOR JEE MAIN 2019 (JANUARY SESSION) Find courses & lessons 735 Courses IIT JEE 2,521 Courses Str Chemistry 797 Courses Details in Plus Tab wwEest HINDI Home My Library Plus Profile SUCCESS IN JEE MAIN ER. VINEET LoOMBA (IIT RooRKEE)

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)

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)

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)

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)

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)

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)