algebra functions and relations

Relations and Functions - In our daily life, we come across many relations such as father-son, brother-sister, teacher-student and many more. In mathematics too, we come across relations such as . A is a subset of B . line l is parallel to line m . number m i..

Summary Relations and Functions - A pair of objects, written in a specified order is called an ordered pair . A pair of objects, written in a specified order is called an ordered pair . For the ordered pair (a,b), a is called the first element and b, the second element. The orde..

Theorem 1..

We consider two sets A and B. We form the Cartesian Product, we form relations. From all the relations, we can select a few which satisfy the rule that each element of the set A is related to only one element of the set B. When a relation satisfies this rul..

Function - Any relation on A x B in which (i) no two second elements have a common first element and (ii) every first element has a corresponding second element is called a function.Any relation on A x B in which (i) no two second elements have a common first..

Summary - A function is a relation on A x B is which A function is a relation on A x B is which (i) no two second elements have a common first element. (ii) every first element has a corresponding second element. Every function is either one-one ont..

(1) One-one function (2) Many-one function (3) Onto function (4) Into function Let the relation be from set A to set ..

(a) (i) The relation should be one-one or many-one, and (ii) Every first element is mapped which means that every pre-image should have an image. (b) For graphs: Draw a line parallel to the y-axis. If it cuts the graph only in one point, then the graph represents a function. If..

The arrow diagram represents a relation from set A to set B. (i) Represent the relation in roster form. (ii) Is this relation a function? Give reason for your answer. (i) {(1, 2), (2, 4), (5, 2), (3, 10), (4, 10)} (ii) Yes it is a function. E..

A function is a relation on A x B is which A function is a relation on A x B is which (i) no two second elements have a common first element. (ii) every first element has a corresponding second element. Every function is either one-one onto or..