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Relation means in the real world how closely they know each other

there are many types of relation

Perfect positive relation -very Close

Positive relation -Close to each-other

Negative relation -Apart from each-other

Perfect negative relation -Very apart

If (a,b)∈R,We can say that a is related to b under the relation R

and mathematically it can be written as aRb

Types of Relation

Empty relation

A relation R in set A is called empty relation if no element of A is related to any element of A

i.e. R=Φ⊂AxA

Universal Relation

A relation R in set A is called \universal relation if each element of A is related to every element of A

R=AXA

Both the empty and universal relation are called trivial relation.

A relation R in set A is called.

1) Reflexive if (a,a)∈R,for every a∈R

2)Symmetric if (a,b)∈R implies that (b,a)∈R for all a,b∈A

3)Transitive if (a,b)∈R and (b,c)∈R implies that (a,c)∈R for all a,b,c∈A

A relation R in set A is called an equivalence relation if R is Reflexive, Symmetric and Transitive.

The function is nothing but the relation between inputs to the possible outputs, where each input is related to precisely one output.

There are various type of function

1)identity function

2)Constant function

3)polynomial function

4)Rational Function

5)Modulus function

6)Signum Function

A function f:x→y is defined to be a One-one or injective function if images of a distinct element of X under f are distinct

for every x1 and x2 ∈ X f(x1)=f(x2)

implies x1=x2

otherwise, function f is called many-one

A function f:x→y is defined to be an On-to or surjective function

if every element of Y is an image of some element of X under function f

for every y∈Y,there exist an element x in X such that f(x)=y

A function f:x→y is said to be one-one and onto (or bijective), if f is both one-one and onto.

Continuous function:

If there are no gaps in the curve or no breakpoint in the curve are called the continuous function

for example f(x)=x2 is continuous function

Discontinuous function:

If there are gaps in the curve or breakpoint in the slider are called the continuous function

f(x)=1/x-1 is discontinuous function