What is the fundamental difference between a relation and a function?

Question:

What is the fundamental difference between a relation and a function? Is every relation a function?

Solution:

Differences between relation and function

1. 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

2. 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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