Let A 345 and D 456 and let R be the divides relation from

Let A = {3,4,5} and D = {4,5,6} and let R be the \"divides\" relation from A to D as follows For all (x, y) epsilon A times b, xRy iff x\\y. Find R and R^-1 explicitly.

Solution

Let us find elements of the form: (3,x)

3|3 and 3|6 , so (3,3),(3,6) are the only elements

(4,4) is another element

(5,5) is another element

So,

R={(3,3),(3,6),(4,4),(5,5)}

R^{-1}={(3,3),(6,3),(4,4),(5,5)}