Given relation $R=\{(x, y): y=x+5, x<4, x, y \in N\}$. Where N is a set of natural numbers then:
Answer & explanation
Correct answer: option 2
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