Question

Determine whether the relation R in the set A = {1,2,3,4,5,6} as R = {x,y}:y is divisible by x is reflexive, symmetric and transitive.

Answer 1

(1) R is reflexive, as (a, a) ∈ R

⇒ a is divisible by a

∴ R is reflexive.

(2) Let (1, 2) ∈ R ⇒ 2 is divisible by 1

But (2,1) ∈ R ⇒ 1 cannot divide by 2

∴ R is not symmetric.

(3) Let (1, 2)∈ R ⇒ 1(2, 4)ER

⇒ 2 is divisible by I and 4 is divisible by 2

Now, (1,4) ∈ R ⇒ 4 is divisible by 1

∴ (1, 2)∈ R I(2,4) ∈ R ⇒ (1, 4)∈ R

∴ R is transitive.