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.
