Question

To calculate the list of ordered pairs defining the relation whose matrix is given as \(\left( {\begin{array}{*{20}{l}}1&1&0&1\\1&0&1&0\\0&1&1&1\\1&0&1&1\end{array}} \right)\)

Short answer

The list of ordered pairs is \(\{ (1,1),(1,2),(1,4),(2,1),(2,3),(3,2),(3,3),(3,4),(4,1),(4,3),(4,4)\} \).

Step-by-step solution

Given data

The matrix of the relation is given as:

\(\left( {\begin{array}{*{20}{l}}1&1&0&1\\1&0&1&0\\0&1&1&1\\1&0&1&1\end{array}} \right)\)

Concept of Matrix

The ordered pair\((i,j)\)belongs to the relation if and only if the\({(i,j)^{th}}\)entry in the matrix is\(1\).

Calculation for the list of ordered pairs

The list of ordered pairs of the relation corresponds to the given matrix is determined in accordance to the definition.

So, the list of ordered pairs is \(\{ (1,1),(1,2),(1,4),(2,1),(2,3),(3,2),(3,3),(3,4),(4,1),(4,3),(4,4)\} \).