Lecture-3 Class 12 Maths

 जिंदगी बहुत कुछ सिखाती है ,
कभी हँसाती है तो कभी रुलाती है ,
पर जो हर हाल में खुश रहते हैं ,
जिंदगी उन्ही के आगे सर झुकाती है।

Lecture - 3 Relations and Functions

Logic for this lecture:

• Functions \subseteq Relations
• A relation from non-empty set A to non-empty set B is said to be function, if
→ every element of set A has only one image in set B.
In other words, Domain = A and
no distinct ordered pairs have same first element.

DIFFERENT MAPPINGS OF FUNCTIONS

One-One / Injective Mapping / Monomorphism

A function is said to be one-one if each member of the range of the function arises for one and only one member of the domain of the function.
• A function f: A → B is said to be one-one if  f(a) = f(b) \Rightarrow a = b

Many-One

A function is said to be many-one if at least one member of the range of the function arises for more than one member of the domain of the function.
• A function f: A → B is said to be one-one if  f(a) = f(b) \Rightarrow a \ne b

Onto Mapping / Surjective Function

• In a Surjective function, 
Range = Co-domain

Into Mapping

• In a Surjective function, 
Range \subset Co-domain

• A function which is both one-one and onto is called Bijective Function.

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