In how many ways a relation can be represented? State two different examples to represent each of them.
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There are 4 ways of representing a relation. The 4 ways are,
- Relation as a matrix
- Relation as an arrow diagram
- Relation as directed graph(Digraph)
- Relation as a table
The following examples illustrate how relations can be represented.
Relation as a matrix
Let P={1,2,3,4}, Q={a, b, c, d}.
R is given as,
R={(1,a),(1,b),(1,c),(2,b),(2,c),(2,d)}. We can represent this Relation in the matrix below,
Let P={1,2,3} and Q={1,2} then its corresponding relation R is given as,
R={(1,1),(1,2),(2,1),(2,2),(3,1),(3,2)}
In matrix form,
Relation as Digraph
Given P={1,2,3,4}, the relation R={(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)}
The digraph for this relation is shown in the image below,
Given A={1,2,3,4}, its relation R is,
R={(1,2),(2,2),(2,4),(3,2),(3,4),(4,1),(4,3)}
The Digraph for this relation is shown in the image below.
Relation as an arrow diagram.
Let P={1,2,3,4}, Q={a, b, c, d}. The relation R={(1,a),(2,a),(3,a),(1,b),(4,b),(4,c),(4,d)}
The arrow diagram for this relation is shown in the image below.
Let R={(1,1),(2,4),(3,9),(4,16),(5,25)}, then the arrow diagram for this relation is shown in the image below.
Relation as a table
Let P=(1,2,3,4) and Q={x, y, z, k}, the relation R={(1,x),(1,y),(2,z),(3,z),(4,k)}
This relation is represented in the table below,
x y z k
1 * *
2 *
3 *
4 *
The Relation R={(-1,1),(0,-2),(3,1),(4,-1)} is represented using the following table
x y
-1 1
0 -2
3 1
4 -1