A relation R in the set A = {1,2,3,4,5,6, } defined as R = {(x, y) :…

A = {1,2,3,4,5,6, } 

R = {(x, y) : y is divisible by x} 

We know that any number x is divisible by itself.

⇒ (x, x) ∈ R

So, R is reflexive,

But, (4, 2) ∉R [as 4 is divisible by 2]

So, R is not symmetric.

Let (x, y), (y, z) ∈ R , then Y is divisible by x and x is divisible by y.

So, z is divisible by x.

⇒ (x, z) ∈ R

So, R is transitive.

Hence, r is reflexive and transitive but not symmetric.