Consider the following adjacency matrix defined on the set X = {10, 20, 30, 40}:1001010000100101Which of the following option correctly represents the Relation defined by the above adjacency matrix?Question 11Answera.R = {(10, 10), (20, 20), (30, 40), (40, 30), (10, 40), (40, 20)}b.R = {(10, 40), (40, 20), (40, 40), (30, 30), (10, 10), (20, 20)}c.R = {(10, 10), (20, 20), (40, 40), (40, 30), (10, 40), (40, 20)}d.R = {(10, 10), (20, 20), (30, 40), (40, 30), (40, 10), (40, 20)}

The adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the adjacency matrix given, a '1' represents the presence of an edge between the vertices and '0' represents the absence of an edge.

The given adjacency matrix is:

1 0 0 1 0 1 0 0 0 0 1 0 1 0 1 0

This matrix is defined on the set X = {10, 20, 30, 40}. The rows and the columns of the matrix represent the elements of the set X in the order in which they are given.

So, the first row and first column represent the element 10, the second row and second column represent the element 20, and so on.

Now, let's find out the pairs for which the value is 1 in the matrix.

• The (1,1) position in the matrix is 1. So, we have the pair (10,10).
• The (2,2) position in the matrix is 1. So, we have the pair (20,20).
• The (3,3) position in the matrix is 1. So, we have the pair (30,30).
• The (4,4) position in the matrix is 0. So, we don't have the pair (40,40).
• The (1,4) position in the matrix is 1. So, we have the pair (10,40).
• The (4,1) position in the matrix is 1. So, we have the pair (40,10).
• The (4,3) position in the matrix is 1. So, we have the pair (40,30).

So, the relation R defined by the adjacency matrix is R = {(10, 10), (20, 20), (30, 30), (10, 40), (40, 10), (40, 30)}. But this option is not given in the choices. So, there seems to be a mistake in the question or the options provided.