Question

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

Answer 1

Every mapping (function) is a relation but every relation is not a mapping.

The relation R is said to be reflexive.

If aR a $\forall aϵA$. (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}

$\therefore R\subset A\times B$