## 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) Biconditional statements If p and q are any two statements then the compound statement in the form of "p if and only if q" is called a biconditional statements and is written in symbolic form p q or p q (i) A number is divisible by 3 if and only if the sum of the digits forming the number is divisible by 3. (ii) One is less than seven if and only if two is less than eight. (iii) A triangle is equilateral if and only if it is equiangular. SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) p q is true only when both p and q have the same value. F T F F Negation of Biconditional statement: SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Write the negation of each of the following statements: Ex.ABC is an equilateral triangle if and only if it is equiangular. Let p ABC is an equilateral triangle q It is equiangular ~(p <q) : Either ABC is an equilateral triangle and it is not equiangular or ABC is not an equilateral triangle and it is equiangular. Ex. Two lines are parallel if and only if they have the same slope Sol. Let p : Two lines are parallel q : They have the same slope (p) -Either two lines are parallel and they not have the same slopes or two lines are not parallel and they have the same slope. 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)

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