Given relation $R=\{(x, y): y=x+5, x<4, x, y \in N\}$. Where N is a set of natural numbers then:

R is transitive but neither reflexive nor symmetric.

The correct answer is Option (2) - R is transitive but neither reflexive nor symmetric.

(1) R is not reflexive

eg; for $(1, 1) ∈N×N$ $1=1+5$ (false)

(2) Not symmetric

eg; $(1,6)∈R$ but $(1,6)∉R$

(3) $(x,y)∈R, (y,z)∈R$

$y=x+5,z=y+5$ so $z=x+10$

but as domain = (1, 2, 3) not possible

⇒ R is transitive