Question

To calculate the matrix \(\bar R\), representing the complement of the relation \(R\), whose matrix is \(R\).

Short answer

The matrix \(\bar R\) is obtained by changes of \(0\) to \(1\) and \(1\) to \(0\) in the matrix \(R\).

Step-by-step solution

Given data

The matrix \(R\) of the relation \(R\).

Concept of Matrix relation

The matrix of the relation is given as:

\({R_{ij}} = 1 \Leftrightarrow (i,j) \in R\) …….(1)

\(R_{ij}^{ - 1} = 1 \Leftrightarrow {R_{ji}} = 1\) …….(2)

Calculation of the matrix 

From (1) and (2), the matrix \(\bar R\) is obtained by changes of \(0\) to \(1\) and \(1\) to \(0\) in the matrix \(R\).