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Question

What is the distinction between a relation and function and when do you call a relation reflexive, symmetric and transitive ?

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Solution

Every mapping (function) is a relation but every relation is not a mapping.
The relation R is said to be reflexive.
If aR a aϵA. (not for all)
The relation R is said to be symmetric.
If aRb then bRa. (not for all a and b).
The relation R is said to be transitive.
If aRb and bRc then aRc (not for all a, b, c)
A relation from a set A to the set B is denoted as
R = {(x, y) :x ϵ A and y ϵ B and x R y}
RA×B

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