One to one and onto functions | Relations and Functions | Class XII | Mathematics | Khan Academy

In this video, we will learn what one to one and onto functions are.
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Created by
Aakash Singh Bagga

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[@Styla-es7dk]

Agr set A main koi akela reh jaye to kya wo one to one function kehlaiye ga?

[@sqnldrhadi]

If in a set \( X \), one element is not related to any element in set \( Y \), then the relation between \( X \) and \( Y \) cannot be a function. In a function, each element in the domain (set \( X \)) must be related to exactly one element in the codomain (set \( Y \)). If there exists an element in \( X \) that is not related to any element in \( Y \), then the relation does not satisfy this requirement of a function.
In other words, for every element \( x \) in \( X \), there must be exactly one element \( y \) in \( Y \) such that \( (x, y) \) is in the function. If there's an \( x \) that does not have any corresponding \( y \), it violates the definition of a function.
So, the type of relation you described would not be a function. It could be a relation, but it wouldn't meet the criteria for a function.

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The function will simply not exist

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Function hi nhi rhega woh then

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[@user-nw7sh1lt2b]

Agr koi fx one one h to wo onto bhi hoga kya ?

[@kritikavishwakarma9293]

Onto can be one-one and vice versa but not necessary it depends on the defined relation

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Thank you sir❤