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what is into function , many to one function ,one -one function

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$I N T O F U N C T I O N : A f u n c t i o n f : A \to B i s a n i n t o f u n c t i o n i f t h e r e e x i s t s a n e l e m e n t i n B h a v i n g n o p r e - i m a g e i n A . I n o t h e r w o r d s, f : A \to B i s a n i n t o f u n c t i o n i f i t i s n o t a n o n t o f u n c t i o n . M A N Y - O N E F U N C T I O N : A f u n c t i o n i s s a i d t o b e a m a n y - o n e f u n c t i o n i f t w o o r m o r e e l e m e n t s o f s e t A h a v e t h e s a m e i m a g e i n B . I n o t h e r w o r d s, f : A \to B i s a m a n y - o n e f u n c t i o n i f i t i s n o t a o n e - o n e f u n c t i o n . O N E - O N E F U N C T I O N : A f u n c t i o n i s s a i d t o b e o n o n i f d i f f e r e n t e l e m e n t s o f A h a v e d i f f e r e n t i m a g e s i n B . T h u s, f i s o n e - o n e \Leftrightarrow a \neq b \Rightarrow f (a)\neq f (b) f o r a l l a, b \in A \Leftrightarrow f (a)= f (b)\Rightarrow a = b f o r a l l a, b \in A$

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