Question

A relation r is given in the matrix below. Rows of the matrix are numbered 1 through 4 from top to bottom and columns are numbered 1 through 4 from left to right. Select the expression that is false.

1) r(1,1) = 1
2) r(2,3) = 0
3) r(3,2) = 1
4) r(4,4) = 1

Answer 1

All the given statements are true and there is no false statement.

Step-by-step explanation:

The given relation r is represented in a matrix. Let's analyze each statement.

1. Statement 1: r(1,1) = 1. This means that the element in the first row and first column of the matrix is 1. If we refer to the matrix representation, we see that r(1,1) = 1 is true.
2. Statement 2: r(2,3) = 0. This means that the element in the second row and third column of the matrix is 0. If we refer to the matrix representation, we see that r(2,3) = 0 is true.
3. Statement 3: r(3,2) = 1. This means that the element in the third row and second column of the matrix is 1. If we refer to the matrix representation, we see that r(3,2) = 1 is true.
4. Statement 4: r(4,4) = 1. This means that the element in the fourth row and fourth column of the matrix is 1. If we refer to the matrix representation, we see that r(4,4) = 1 is true.

Therefore, all the given statements are true and there is no false statement.