Relation R in the set A = {1, 2, 3, 4, 5, 6} as
R = {(x, y) : y is divisible by x}

Question

Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y) : y is divisible by x}

Philoid · Accepted Answer

It is given that relation R in the set A = {1, 2, 3, 4, 5, 6} as

R = {(x, y) : y is divisible by x}

We know that any number (x) is divisible by itself.

⇒ (x,x) ϵ R

⇒ R is reflexive.

Now, (2,4) ϵ R but (4,2) ∉ R.

⇒ R is not symmetric.

Let (x,y), (y,z) ϵ R. Then, y is divisible x and z is divisible by y.

⇒ z is divisible by x.

⇒ (x,z) ϵ R

⇒ R is transitive.

Therefore, R is reflexive and transitive but not symmetric.

Relation R in the set A = {1, 2, 3, 4, 5, 6} asR = {(x, y) : y is divisible by x}