Relation R in the set N of natural numbers defined as
R = {(x, y) : y = x + 5 and x < 4}

Question

Relation R in the set N of natural numbers defined as R = {(x, y) : y = x + 5 and x < 4}

Philoid · Accepted Answer

It is given that Relation R in the set N of natural numbers defined as

R = {(x, y) : y = x + 5 and x < 4}

we can see that (1,1) ∉ R

⇒ R is not reflexive.

Now, (1,6) ϵ r but (6,1) ∉ R.

⇒ R is not symmetric.

Now, there is no pair in R such that (x,y) and (y,z) ϵ R, then (x,z) ∉ R.

⇒ R is not transitive.

Therefore, R is neither reflexive, nor symmetric, nor transitive.

Relation R in the set N of natural numbers defined asR = {(x, y) : y = x + 5 and x < 4}