Relations –

Arrow Diagrams

Let us consider the statement, “the Tiger is the national animal for India & Bangladesh, Kangaroo is the national animal of Australia, the Lion that of Belgium, and Zebra is national animal of Botswana” we can draw the following arrow diagram to represent it .

The countries (the elements of the first set) and the animals ( the elements of the second set) are linked by a relation “ national animal is ”. The arrows are drawn between the ordered pairs, or matching pairs, of elements that satisfy the relations.

A relation is a link between the elements of two sets based on some common property. We know the two ways of representing relations – by making arrow diagrams and by expressing in the roster form.


Roster Form

Let us call the set of animals A and the set of countries B, to express the relations between the two sets in the roster form, we write the matching, or ordered pairs (India, Tiger), (Bangladesh, Tiger), (Australia, Kangaroo), (Botswana, Zebra). Then the pair (India, Tiger) means “India’s national animal is Tiger”. Thus we get –

A = {India, Bangladesh, Australia, Botswana}, B = {Tiger, Kangaroo, Zebra} and R = {(India, Tiger), (Bangladesh, Tiger), (Australia, Kangaroo), (Botswana, Zebra)}. Where R is the relation from the set A to the set B.