Example for Symbolic Relationships

Introduction:
         We use the term ‘relation’ to unite two persons like ‘is son of’, ‘is father of’, ‘is brother of’, ‘is sister of’, etc. or to unite two objects by means of ‘is shorter than’, ‘is bigger than’, etc. When comparing (relate) the objects (human beings) the idea of relation becomes extremely essential. In Mathematics, Relationship is a similar fashion that we connect two sets (set of objects) by means of relation. Let us see symbolic relationship in this article.

Mathematical Symbolic Relationships:

Let A and B be any two sets. A relation from A → B (read as A to B) is a subset of the Cartesian product A × B. This is the way to represent symbolic relationship.

Examples of Symbolic Relationships:

Solution:
            Since relation from A to B is a subset of the Cartesian product
            A × B = {(1 , a) , (1, b) , (2 , a) , (2 , b)} any subset of A × B is a relation from A → B.
     ∴    {(1 , a), (1 , b), (2 , a), (2 , b)}, {(1, a), (1, b)}, {(1, b, (2, b)}, {(1 , a)} are some relations from A to B.
            Similarly any subset of B × A = {(a, 1), (a, 2), (b, 1), (b, 2)} is a relation from B to A.
            {(a, 1), (a, 2), (b, 1), (b, 2)}, {(a, 1), (b, 1)}, {(a, 2), (b, 1)} are some relations from B to A.