Types of Relations
There are four types of relations as follows: (i) one - one (ii) many - one (iii) one - many (iv) many - ma..
Summary Linear equations in two variables
An equation is called a Linear equation in one variable or an equation of degree one in one variable, if only a single variable with degree one occurs in the equation. An equation is called a Linear equation in one variable or an equation of de..
Types of Functions (Mapping)
The following are the Types of Functions or Mapping: (1) One-one function (2) Many-one function (3) Onto function (4) Into functio..
Test for Functions (Summary)
The relation should be one-one or many-one, and Every first element is mapped which means that every pre-image should have an imag..
Types of Relations
Types of Relations - There are four types of relations as follows:There are four types of relations as follows: (i) one - one (ii) many - one (iii) one - many (iv) many - m..
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 onto or one-one into or many-one..
4. Into function
There is at least one element of B which has no pre-image. In above fig.(i) the function is one-one and into, while in fig.(ii) the function is many-one and into. For types of functions, the four arrow diagrams given for one-one and many-one ..
There is at least one element of B which has no pre-image. In above fig.(i) the function is one-one and into, while in fig.(ii) the function is many-one and into. For types of functions, the four arrow diagrams given for one-one and many-one ..Examples:
(1) 2x 2 -1 = 0 (2) x 2 -5x+7 = 0 The solution to quadratic equations can be found using various techniques. One of them being, graph..
3. Onto function
Every element of the set B has at least one pre-image. In above fig.(i), the function is one-one and onto, while in fig.(ii) the function is many-one and on..
Every element of the set B has at least one pre-image. In above fig.(i), the function is one-one and onto, while in fig.(ii) the function is many-one and on..Theorems on Relations and Functions
Theorem 1..
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