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Question
What is the fundamental difference between a relation and a function? Is every relation a function?
Solution
Differences between relation and function
- If R is a relation from A to B, then domain of R may be a subset of A. But if f is a function from A to B, then domain f is equal to A.
- In a relation from A to B, an element of A may be related to more than one element in B. But in a function from A to B, each element of A must be associated to one and only one element of B.
Thus, every function is a relation, but every relation is not necessarily a function.
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