Let R1 and R2 be the divides and is a multiple of relations

Let R1 and R2 be the “divides” and “is a multiple of” relations on the set of all positive integers, respectively. That is R1 = {(a, b) | a divides b} and R2 = {(a, b) | a is a multiple of b}. Find

a) R1 R2

b) R1 R2

c) R1 R2

d) R2 R1

e) R1 R2

Solution

a. R1R2
{(a,b)| a divides b or a is a multiple of b}
b. R1R2
{(a,b)| a divides b and a is a multiple of b} = {(x,x)|xZ+}
c. R1-R2
{(a,b)| a divides b, but is not equal to b}
d. R2-R1
{(a,b)| a divides b, but is not equal to b}