tag:blogger.com,1999:blog-76533956341077923902024-03-20T00:49:12.536-07:00Learning Mathematics for IIT JEEKVSSNraohttp://www.blogger.com/profile/05748254811752425330noreply@blogger.comBlogger604125tag:blogger.com,1999:blog-7653395634107792390.post-37319880036035165382021-12-22T20:00:00.018-08:002021-12-22T22:08:07.210-08:00Index to Notes of Chapters in R.D Sharma - JEE Mathematics Objective Book<div><div>IN MEMORY OF</div><div><br /></div><div>MY FATHER</div><div><br /></div><div>GANGADHARA SASTRY</div><div><br /></div><div>HE TAUGHT ME MATHEMATICS IN X CLASS</div></div><div><br /></div><div><a href="https://iit-jee-maths.blogspot.com/2017/12/shri-kvss-gangadhara-sastry-kakinada.html" target="_blank">Shri K.V.S.S. Gangadhara Sastry, Kakinada</a></div><div><br /></div><div><br /></div>1. <a href="https://iit-jee-maths.blogspot.com/2008/06/ch-1-sets-concept-review.html" target="_blank">Sets</a> <div>2. <a href="https://iit-jee-maths.blogspot.com/2008/06/ch-2-cartesian-product-of-sets.html" target="_blank">Cartesian product of sets and relations</a> </div><div>3. <a href="https://iit-jee-maths.blogspot.com/2008/06/ch-3-functions-concept-review.html" target="_blank">Functions</a> </div><div>4. <a href="https://iit-jee-maths.blogspot.com/search/label/Binary%20operations" target="_blank">Binary operations</a> </div><div><br /></div><div>5. <a href="https://iit-jee-maths.blogspot.com/2008/05/chapter-5-complex-numbers.html" target="_blank">Complex numbers</a> </div><div>6. <a href="https://iit-jee-maths.blogspot.com/search/label/Sequences" target="_blank">Sequences and series</a> </div><div>7. <a href="https://iit-jee-maths.blogspot.com/search/label/Quadratic%20equations" target="_blank">Quadratic equations and expressions</a> </div><div>8. <a href="https://iit-jee-maths.blogspot.com/search/label/Permutations-combinations" target="_blank">Permutations and Combinations</a> </div><div>9. <a href="https://iit-jee-maths.blogspot.com/search/label/Binomial%20theorem" target="_blank">Binomial theorem</a> </div><div>10. <a href="https://iit-jee-maths.blogspot.com/search/label/Exponential%20and%20logarithmic%20series" target="_blank">Exponential and logarithmic series</a> </div><div>11. <a href="https://iit-jee-maths.blogspot.com/search/label/Matrices" target="_blank">Matrices</a> </div><div>12. <a href="https://iit-jee-maths.blogspot.com/search/label/Determinants" target="_blank">Determinants</a> </div><div><br /></div><div>13. <a href="https://iit-jee-maths.blogspot.com/search/label/Cartesian%20system" target="_blank">Cartesian System of Rectangular Coordinates and straight lines</a> </div><div>14. <a href="https://iit-jee-maths.blogspot.com/search/label/Family%20of%20lines" target="_blank">Family of lines</a> </div><div>15. <a href="https://iit-jee-maths.blogspot.com/search/label/Circle" target="_blank">Circle </a></div><div>16. <a href="https://iit-jee-maths.blogspot.com/search/label/Parabola" target="_blank">Parabola</a> </div><div>17. <a href="https://iit-jee-maths.blogspot.com/search/label/Ellipse" target="_blank">Ellipse</a> </div><div>18. <a href="https://iit-jee-maths.blogspot.com/search/label/Hyperbola" target="_blank">Hyperbola</a> </div><div><br /></div><div>19. <a href="https://iit-jee-maths.blogspot.com/search/label/Real%20functions" target="_blank">Real Functions</a> </div><div>20. <a href="https://iit-jee-maths.blogspot.com/search/label/Limits" target="_blank">Limits</a> </div><div>21. <a href="https://iit-jee-maths.blogspot.com/search/label/Continuity%20and%20Differentiability" target="_blank">Continuity and Differentiability</a> </div><div>22. <a href="https://iit-jee-maths.blogspot.com/search/label/Differentiation" target="_blank">Differentiation</a> </div><div>23. <a href="https://iit-jee-maths.blogspot.com/search/label/Tangents%20and%20normals" target="_blank">Tangents, Normals and other applications of derivatives </a></div><div>24. Increasing and decreasing functions </div><div>25. <a href="https://iit-jee-maths.blogspot.com/search/label/Maxima%20and%20minima" target="_blank">Maximum and minimum values</a> </div><div>26. <a href="https://iit-jee-maths.blogspot.com/search/label/Indefinite%20integrals" target="_blank">Indefinite integrals</a> </div><div>27. <a href="https://iit-jee-maths.blogspot.com/search/label/Definite%20integrals" target="_blank">Definite Integration</a> </div><div>28. <a href="https://iit-jee-maths.blogspot.com/search/label/Area%20of%20bounded%20regions" target="_blank">Areas of Bounded regions</a> </div><div>29. <a href="https://iit-jee-maths.blogspot.com/search/label/Differential%20equations" target="_blank">Differential equations</a> </div><div><br /></div><div>30. <a href="https://iit-jee-maths.blogspot.com/search/label/Vector%20algebra" target="_blank">Vectors </a> </div><div>31. <a href="https://iit-jee-maths.blogspot.com/search/label/Three%20dimensional%20geometry" target="_blank">Three Dimensional Geometry </a> </div><div>32. <a href="https://iit-jee-maths.blogspot.com/search/label/Probability" target="_blank">Probability</a> </div><div><br /></div><div>33. <a href="https://iit-jee-maths.blogspot.com/search/label/Trigonometric%20ratios" target="_blank">Trigonometric ratios</a>, Identities and Maximum & Minimum Values of Trigonometrical Expressions 34. <a href="https://iit-jee-maths.blogspot.com/search/label/Properties%20of%20triangles" target="_blank">Properties of Triangles and circles connected with them</a> </div><div>35. <a href="https://iit-jee-maths.blogspot.com/search/label/Trigonometric%20equations" target="_blank">Trigonometrical equations</a> </div><div>36. <a href="https://iit-jee-maths.blogspot.com/search/label/Inverse%20trigonometric%20functions" target="_blank">Inverse Trigonometrical functions </a></div><div>37. <a href="https://iit-jee-maths.blogspot.com/search/label/Solutions%20of%20triangles" target="_blank">Solution of Triangles</a> </div><div>38. <a href="https://iit-jee-maths.blogspot.com/search/label/Heights%20and%20distances" target="_blank">Heights and distances</a></div><div><br /></div><div><br /></div><div><br /></div><div>Updated on 23 Dec 2021, 20 June 2021 - Father's Day</div><div>First published 18 Dec 2011</div>KVSSNraohttp://www.blogger.com/profile/05748254811752425330noreply@blogger.com0tag:blogger.com,1999:blog-7653395634107792390.post-31768753862567872012021-12-22T17:27:00.000-08:002021-12-22T21:45:40.575-08:00Shri K.V.S.S. Gangadhara Sastry, Kakinada<br />
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<a href="https://2.bp.blogspot.com/-KztzO_O9MSc/Wj2wTGTyapI/AAAAAAAABdk/Ror9T7pxvJUxtXPtwdIAY7ThwFpdjPD9gCLcBGAs/s1600/kvssgs-23dec17.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="640" src="https://2.bp.blogspot.com/-KztzO_O9MSc/Wj2wTGTyapI/AAAAAAAABdk/Ror9T7pxvJUxtXPtwdIAY7ThwFpdjPD9gCLcBGAs/s640/kvssgs-23dec17.jpg" width="480" /></a></div>
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<br />You were a light<br />that always glowed bright<br />You were a scholar erudite<br />gave your students insight<br /><br />You had knowledge might<br />used to it well to write<br />notes and essays right<br />that brought students delight<br /><br />You had the foresight<br />to plan and excite<br />your children and students to recite<br />poems full of wisdom and wit<br /><br />by K.V.S.S. Narayana Rao<br />23.12.2014<br /><div><br /></div><div><br /></div><div>
Worked in P.R.G.C. Higher Secondary School, Kakinada from 1960 to 1973<br />
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Worked as Head Master, P.R.G. Middle School, Kakinada - 1977 to 1979<br />
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I learned mathematics in X Class from him.<br />
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Guru Devebhyo Namah<br />
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Learning Companions for Class XI and XII and JEE<br />
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<a href="http://iit-jee-maths.blogspot.com/2017/12/cbse-mathematics-class-11-syllabus.html" target="_blank">http://iit-jee-maths.blogspot.com/2017/12/cbse-mathematics-class-11-syllabus.html</a></div><div><br /></div><div><br /></div><div>Ud. 23.12.2021</div><div>Pub 23.12.2017</div>KVSSNraohttp://www.blogger.com/profile/05748254811752425330noreply@blogger.com0tag:blogger.com,1999:blog-7653395634107792390.post-79289053868953139442017-12-22T19:03:00.000-08:002017-12-22T19:03:22.769-08:00CBSE Class XI - chap. I-3. Trigonometric Functions - Learning Companion<br />
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3. Trigonometric Functions<br />
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Positive and negative angles. Measuring angles in radians and in degrees and conversion of one into other.<br />
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Definition of trigonometric functions with the help of unit circle. Truth of the sin2x+cos2x=1, for all x. Signs of trigonometric functions. Domain and range of trignometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application. Deducing identities like the following:<br />
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Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x. General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.<br />
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Maths Trigonometry part 1 (Basic Concepts, Why Trigonometry) CBSE class 11 Mathematics XI<br />
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<iframe allow="encrypted-media" allowfullscreen="" frameborder="0" gesture="media" height="315" src="https://www.youtube.com/embed/672-Zb7EhcI" width="560"></iframe>
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ExamFear Education<br />
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Maths Trigonometry part 2 (Degree Measure) CBSE class 11 Mathematics XI<br />
<a href="https://www.youtube.com/watch?v=1FijJ6tuqW4" target="_blank">https://www.youtube.com/watch?v=1FijJ6tuqW4</a><br />
<br />
Maths Trigonometry part 3 (Radian Measure) CBSE class 11 Mathematics XI<br />
<a href="https://www.youtube.com/watch?v=Bleq2RyPFUE" target="_blank">https://www.youtube.com/watch?v=Bleq2RyPFUE</a><br />
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<br />KVSSNraohttp://www.blogger.com/profile/05748254811752425330noreply@blogger.com0tag:blogger.com,1999:blog-7653395634107792390.post-13185600940501278252017-12-22T18:11:00.000-08:002017-12-22T18:11:19.612-08:00CBSE Class XI - Chap2. Relations and Functions<br />
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2. Relations & Functions<br />
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Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets.<br />
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Cartesian product of the sets of real (upto R x R). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain and range of a function. Real valued functions, domain and range of these functions: constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotients of functions.<br />
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_______________<br />
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<iframe allow="encrypted-media" allowfullscreen="" frameborder="0" gesture="media" height="315" src="https://www.youtube.com/embed/9UqlgOO5gak" width="560"></iframe>
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Relations & Functions<br />
<a href="https://www.youtube.com/watch?v=OxZ0JL4Bjzk" target="_blank">https://www.youtube.com/watch?v=OxZ0JL4Bjzk</a>KVSSNraohttp://www.blogger.com/profile/05748254811752425330noreply@blogger.com0tag:blogger.com,1999:blog-7653395634107792390.post-37527418570289690022017-12-22T17:44:00.000-08:002017-12-22T17:44:28.329-08:00CBSE Class XI - 1. Sets - Learning Companion<br />
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1. Sets<br />
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Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement Sets. Practical Problems based on sets.<br />
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__________________<br />
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<iframe allow="encrypted-media" allowfullscreen="" frameborder="0" gesture="media" height="315" src="https://www.youtube.com/embed/56lqIz7Z_c8" width="560"></iframe>
__________________<br />
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More Youtube Videos<br />
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Videos<br />
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Sets and Relations - Sets | Mathematics | Class 11 | IIT JEE Main + Advanced | askIITians<br />
<a href="https://www.youtube.com/watch?v=uycjFD6KlT4" target="_blank">https://www.youtube.com/watch?v=uycjFD6KlT4</a>KVSSNraohttp://www.blogger.com/profile/05748254811752425330noreply@blogger.com0tag:blogger.com,1999:blog-7653395634107792390.post-9632294277774248072017-12-22T17:34:00.001-08:002017-12-22T19:12:12.655-08:00CBSE Mathematics Class 11 Syllabus and Learning Materials<br />
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Mathematics Class 11 Syllabus<br />
Exam Structure<br />
Unit<span style="white-space: pre;"> </span>Topic<span style="white-space: pre;"> </span>Marks<br />
I.<span style="white-space: pre;"> </span>Sets and Functions<span style="white-space: pre;"> </span>29<br />
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<a href="http://iit-jee-maths.blogspot.com/2017/12/cbse-class-xi-1-sets-learning-companion.html" target="_blank">CBSE Class XI - 1. Sets - Learning Companion</a><br />
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II.<span style="white-space: pre;"> </span>Algebra<span style="white-space: pre;"> </span>37<br />
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III.<span style="white-space: pre;"> </span>Coordinate Geometry<span style="white-space: pre;"> </span>13<br />
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IV.<span style="white-space: pre;"> </span>Calculus<span style="white-space: pre;"> </span>06<br />
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V.<span style="white-space: pre;"> </span>Mathematical Reasoning<span style="white-space: pre;"> </span>03<br />
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VI.<span style="white-space: pre;"> </span>Statistics and Probability<span style="white-space: pre;"> </span>12<br />
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<span style="white-space: pre;"> </span>Total <span style="white-space: pre;"> </span>100<br />
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Unit-I: Sets and Functions<br />
1. Sets<br />
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Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement Sets. Practical Problems based on sets.<br />
<a href="http://iit-jee-maths.blogspot.com/2017/12/cbse-class-xi-1-sets-learning-companion.html" target="_blank"><br /></a>
<a href="http://iit-jee-maths.blogspot.com/2017/12/cbse-class-xi-1-sets-learning-companion.html" target="_blank">CBSE Class XI - 1. Sets - Learning Companion</a><br />
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2. Relations & Functions<br />
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Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets. Cartesian product of the sets of real (upto R x R). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain and range of a function. Real valued functions, domain and range of these functions: constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotients of functions.<br />
<br />
3. Trigonometric Functions<br />
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Positive and negative angles. Measuring angles in radians and in degrees and conversion of one into other. Definition of trigonometric functions with the help of unit circle. Truth of the sin2x+cos2x=1, for all x. Signs of trigonometric functions. Domain and range of trignometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application. Deducing identities like the following:<br />
<br />
Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x. General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.<br />
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Unit-II: Algebra<br />
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1. Principle of Mathematical Induction<br />
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Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications.<br />
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2. Complex Numbers and Quadratic Equations<br />
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Need for complex numbers, especially √1, to be motivated by inability to solve some of the quardratic equations. Algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system. Square root of a complex number.<br />
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3. Linear Inequalities<br />
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Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Graphical solution of system of linear inequalities in two variables.<br />
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4. Permutations and Combinations<br />
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Fundamental principle of counting. Factorial n. (n!)Permutations and combinations, derivation of formulae and their connections, simple applications.<br />
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5. Binomial Theorem<br />
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History, statement and proof of the binomial theorem for positive integral indices. Pascal's triangle, General and middle term in binomial expansion, simple applications.<br />
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6. Sequence and Series<br />
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Sequence and Series. Arithmetic Progression (A.P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P., Arithmetic and Geometric series infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M. Formula for the following special sum:<br />
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Unit-III: Coordinate Geometry<br />
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1. Straight Lines<br />
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Brief recall of two dimensional geometry from earlier classes. Shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form. General equation of a line. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line.<br />
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2. Conic Sections<br />
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Sections of a cone: circles, ellipse, parabola, hyperbola; a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.<br />
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3. Introduction to Three–dimensional Geometry<br />
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Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.<br />
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Unit-IV: Calculus<br />
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1. Limits and Derivatives<br />
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Derivative introduced as rate of change both as that of distance function and geometrically.<br />
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Intutive idea of limit. Limits of polynomials and rational functions, trignometric, exponential and logarithmic functions. Definition of derivative, relate it to slope of tangent of a curve, derivative of sum, difference, product and quotient of functions. The derivative of polynomial and trignometric functions.<br />
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Unit-V: Mathematical Reasoning<br />
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1. Mathematical Reasoning<br />
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Mathematically acceptable statements. Connecting words/ phrases - consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through variety of examples related to real life and Mathematics. Validating the statements involving the connecting words difference between contradiction, converse and contrapositive.<br />
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Unit-VI: Statistics and Probability<br />
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1. Statistics<br />
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Measures of dispersion; Range, mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.<br />
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2. Probability<br />
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Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, 'not', 'and' and 'or' events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with the theories of earlier classes. Probability of an event, probability of 'not', 'and' and 'or' events.KVSSNraohttp://www.blogger.com/profile/05748254811752425330noreply@blogger.com0tag:blogger.com,1999:blog-7653395634107792390.post-72071842854994103792016-05-08T07:04:00.001-07:002016-05-08T07:04:24.427-07:00XII - 11.24 Solution of a homogeneous system of linear equations - Video Lectures<br />
Solving a Homogeneous System<br />
NightingaleMath<br />
__________________<br />
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<iframe allowfullscreen="" frameborder="0" height="480" src="https://www.youtube.com/embed/RZmJKqCOksw" width="640"></iframe>
__________________KVSSNraohttp://www.blogger.com/profile/05748254811752425330noreply@blogger.com0tag:blogger.com,1999:blog-7653395634107792390.post-56671553537158517222016-05-08T06:13:00.001-07:002016-05-08T06:13:12.122-07:00XII - 11.23 Rank method - Video Lectures<div dir="ltr" style="text-align: left;" trbidi="on">
9 May<br />
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A number r is said to be the rank of a an "m x n" marix if<br />
i) every square sub matrix of it of order (r+1) or more is singular, and<br />
ii) there exists at least on square matrix of order r which is non-singular.<br />
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In other words, the rank of a m x n matrix is the order of the highest order non-singular square submatrix of it.<br />
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Solving 4x4 Linear Equations by Rank of Matrix Method_Detailed Step by Step Explanation<br />
Sujoy Krishna Das<br />
__________________<br />
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<iframe allowfullscreen="" frameborder="0" height="360" src="https://www.youtube.com/embed/cXFbClWdiAk" width="640"></iframe>
__________________</div>
KVSSNraohttp://www.blogger.com/profile/05748254811752425330noreply@blogger.com0tag:blogger.com,1999:blog-7653395634107792390.post-16185975979505459272016-05-08T06:06:00.001-07:002016-05-08T06:06:14.459-07:00XII - 11.22 Solution of a non-homogeneous system of linear equations - Video Lectures<div dir="ltr" style="text-align: left;" trbidi="on">
9 May<br />
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Non-Homogeneous system of equation with infinite solution<br />
Rahul Abhang<br />
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<iframe allowfullscreen="" frameborder="0" height="480" src="https://www.youtube.com/embed/rAqfNZT2ndQ" width="640"></iframe>
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Nonhomogeneous System Solutions<br />
TheTrevTutor<br />
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<iframe allowfullscreen="" frameborder="0" height="360" src="https://www.youtube.com/embed/axkmcrVdQPc" width="640"></iframe>
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KVSSNraohttp://www.blogger.com/profile/05748254811752425330noreply@blogger.com0tag:blogger.com,1999:blog-7653395634107792390.post-5098773610319271542016-05-08T06:00:00.000-07:002016-05-08T06:00:01.494-07:00XII - 11.21 System of simultaneous linear equations - Video Lectures<div dir="ltr" style="text-align: left;" trbidi="on">
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Consistency of a System of Linear Equations<br />
MathDoctorBob<br />
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<iframe allowfullscreen="" frameborder="0" height="360" src="https://www.youtube.com/embed/7QGDi6gRtFU" width="640"></iframe>
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Consistent And Inconsistent System of Equations Example - 1 / Matrices / Maths Algebra<br />
We Teach Academy Maths<br />
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<iframe allowfullscreen="" frameborder="0" height="360" src="https://www.youtube.com/embed/7njI8Rfrfns" width="640"></iframe>
__________________</div>
KVSSNraohttp://www.blogger.com/profile/05748254811752425330noreply@blogger.com0tag:blogger.com,1999:blog-7653395634107792390.post-56191541607694755802016-05-08T05:09:00.000-07:002016-05-08T05:09:03.238-07:00XI - 2.4 Some results on relations - Video Lectures1. If R and S are two equivalence relations on a set A, then R∩S is also an equivalence relation on A.<br />
2. The union of two equivalence relations on a set is not necessarily an equivalence relation on the set.<br />
3. If R is an equivalence relation on a set A, the R<sup>-1</sup> is also an equivalence relation on A.<br />
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Proof of Set operations in Relations -1 / NCERT Std XI Mathematics<br />
MathsMynd<br />
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________________KVSSNraohttp://www.blogger.com/profile/05748254811752425330noreply@blogger.com0tag:blogger.com,1999:blog-7653395634107792390.post-3106905554936743622016-05-08T05:01:00.001-07:002016-05-08T05:01:19.818-07:00XI - 2.5 Composition of relations - Video Lectures<br />
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When r and S are two relations from set A to B and B to C respectively, we can define a relation SoR from A to C such that<br />
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(a.c) Є SoR imples for all b Є B subject to the relations (a,b) ЄR and (b.c) ЄS.<br />
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SoR is called the composition of R and S.<br />
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Properties of SoR<br />
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In general RoS is not equal to SoR.<br />
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(SoR) <sup>-</sup> = R<sup>-</sup>oS<sup>-</sup><br />
<sup><br /></sup>
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<span style="font-size: 13.3333px;">Composition of relations</span><br />
<span style="font-size: 13.3333px;">Math 290, GMU </span><br />
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Elementary Linear Algebra: Echelon Form of a Matrix, Part 1<br />
James Hamblin<br />
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Operations that Produce Row Equivalent Matrices<br />
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Maths Relation and Functions Part 1 (Relation function concept) Mathematics CBSE Class X1<br />
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Number of functions<br />
Gate Lectures by Ravindrababu Ravula<br />
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Example On Equal Functions / Maths Algebra<br />
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Domain, Codomain, and Range<br />
Worldwide Center of Mathematics<br />
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Functions, Lecture 4 , Maths IIT JEE ( Definition of functions)<br />
Collegepedia.in<br />
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Composition of Functions<br />
ProfRobBob<br />
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Inverse elements for Binary operations : ExamSolutions Maths Revision<br />
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Inverse Functions<br />
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Properties of the Inverse Image of a Function on Sets: Practice With Proof<br />
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XI -<br />
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2.3 Types of relations - Video Lectures<br />
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2.3 Types of relations<br />
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Void relation<br />
Universal relation<br />
Identity relation<br />
Reflexive relation<br />
Symmetric relation<br />
Transitive relation<br />
Antisymmetric relation<br />
Equivalence relation<br />
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________________<br />
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XI - 2.2 Relations - Video Lectures<br />
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2.2 Relation<br />
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Let A and B be two sets. Then a relation R from A to B is a subset of A×B.<br />
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R is a relation from A to B => R is a subset of A×B.<br />
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Total number of relations: If A and B are two non empty sets with m and n elements respectively, A×B consists of mn ordered pairs.<br />
Since each subset defines a relation from A to B, so total number of relations from A to B is 2<sup>mn</sup>.<br />
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