Chapter 1 Relations and Functions - NCERT Class 12 Mathematics
Chapter 1: RELATIONS AND FUNCTIONS
Screen readable NCERT Class 12 Mathematics Text Book for blind and visually impaired students.
This Chapter is planned, organized and described by Dr T K Bansal for visually impaired and blind students. All efforts have been made to make the chapter fully accessible by providing headings, describing figures and tables. The Chapter has been so designed that the students should enjoy studying this chapter and should move forward without any hurdles. The chapter has been thoroughly checked for any mistakes, still if you find any mistakes or have any suggestions to make it better, please write to us at ‘ blind2Visionary@gmail.com ‘. Your efforts will be highly appreciated.
Do you know that this chapter has 125 examples and problems for you to solve. These problems are distributed as under:
Solved Examples: 51
Exercise 2.1: 16
Exercise 2.2: 12
Exercise 2.3: 14
Exercise 2.4: 13
Misc Exercise: 19
Total : 125
In case you master these questions, you don't need practisng any more problems from any other source.
Table of symbols used in this chapter:
| Symbol | Known As | Used For | Description |
|---|---|---|---|
| ∈ | Element of | Element of a set | Epsilon, a Greek letter |
| × | Times | Multiplication | Normal cross sign |
| φ | fi | Null set | Phi a greek letter |
| ⇒ | Rightwords double arrow | Implies | A right words arrow to = sign |
| ∉ | Not an element of | Not an element of | An epsilon with a cross |
| ± | Plus or minus | Plus or minus | A plus sign above a minus sign |
| ≠ | Not equal to | Not equal to | Equal to sign with a forward slash on it |
| ∪ | Union | Union of 2 sets | Like a capital U |
| ≥ | Greater than or equal to | Greater than or equal to | Greater than sign with a parallel line to the lower arm of greater than sign |
| ∩ | Intersection | Intersection of 2 sets | Like an inverted capital U |
| ′ | Prime | Making two values different | Like ‘ sign |
| ≤ | Less than or equal to | Less than or equal to | Less than sign with a parallel line to the lower arm of less than sign |
| ⊂ | Subset of | Subset of | Like letter c of English alphabet |
| → | Rightwards arrow | Goes to | A rightwards arrow |
| ∀ | for all | For all | Like an upside down capital A |
| ^ | Carrot | Raise to power | Like a birthday cap |
| √ | Square root | Square root | The radical sign used for square root |
| ∞ | Infinity | Infinity | A horizontally lying number 8 o Indoarabic numeral |
| ÷ | Divided by | Division | Dots above and below a dash sign |
| ∨ | Logical or | Logical OR | a plus surrounded by a circle |
| ∧ | Logical and | Logical AND | a dot surrounded by circle |
| π | pi | Ratio of perimeter to the diameter of a circle | A greek letter |
| ∃ | There exists | There exists | Like inverted number 3 |
There is no permanent place in the world for ugly mathematics ... . It may be very hard to define mathematical beauty but that is just as true of beauty of any kind, we may not know quite what we mean by a beautiful poem, but that does not prevent us from recognising one when we read it.
G H HARDY
Lejeune Dirichlet
(1,805-1,859)