Question

Let \(A=\\{0,1,2,3,4,5\\} .\) Write out the relation \(R\) that expresses \(>\) on \(A .\) Then illustrate it with a diagram.

Short answer

The relation \(R\) for '>' on set \(A\) is \(R=\{(1,0), (2,0), (2,1), (3,0), (3,1), (3,2), (4,0), (4,1), (4,2), (4,3), (5,0), (5,1), (5,2), (5,3), (5,4)\}\)

Step-by-step solution

Understand the Relation

The relationship given here is the 'greater than' or '>' relation over the set \(A=\{0,1,2,3,4,5\}\). The pairs of elements from the set \(A\), where the first element is greater than the second element, form this relation.

Identify the Pairs

No pair can be formed with 0 as the first element, because 0 is not greater than any other number in the set. From 1 to 5 we can form following pairs such that the first element is greater than the second one: (1,0), (2,0), (2,1), (3,0), (3,1), (3,2), (4,0), (4,1), (4,2), (4,3), (5,0), (5,1), (5,2), (5,3), (5,4). Hence the relation 'R' for '>' can be written as \(R=\{(1,0), (2,0), (2,1), (3,0), (3,1), (3,2), (4,0), (4,1), (4,2), (4,3), (5,0), (5,1), (5,2), (5,3), (5,4)\}\)

Draw the Diagram

The diagram or graph representing the greater than relation on set \(A\) can be drawn by making six dots or vertices (0 to 5) representing the numbers in set A and draw directed arrows from the 'greater' number to the 'lesser' number for each pair in the relation \(R\).