Then some
of the examples of relations from A to B are
(i)
{(a, b) ∈ A × B: a is brother of b},
(ii)
{(a, b) ∈ A × B: a is sister of b},
(iii)
{(a, b) ∈ A × B: age of a is greater than age of b},
(iv)
{(a, b) ∈ A × B: total marks obtained by a in the final examination is less than
the total marks obtained by b in the final examination},
(v)
{(a, b) ∈ A × B: a lives in the same locality as b} However, abstracting from
this, we define mathematically a relation R from A to B as an arbitrary subset
of A × B If (a, b) ∈ R, we say that a is related to b under the relation R and we write as
a R b In general, (a, b) ∈ R, we do not bother whether there is a recognisable
connection or link between a and b