



 
Hi san, A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y. That is, given an element x in X, there is only one element in Y that x is related to. For example, consider the following sets X and Y. I'll give you a relation between them that is not a function, and one that is.
This relation is not a function from X to Y because the element 2 in X is related to two different elements, b and c. (Note, if you transpose the ordered pairs you <i>would</i> have a function from Y to X  can you see WHY?)
This is a function since each element from X is related to only one element in Y. Note that it is okay for two different elements in X to be related to the same element in Y. It's still a function, it's just not a onetoone function. Hope this helps,  


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