For the set of all straight lines in a plane, the relation of "perpendicularity" is:

A. reflexive but neither symmetric nor transitive.
B. symmetric but neither reflexive nor transitive.
C. transitive but neither reflexive nor symmetric
D. neither reflexive nor symmetric nor transitive.
E. reflexive, symmetric but not transitive.

Choose the correct answer from the options given below:

B only

The correct answer is Option (2) → B only

Let $R:\{(x,y):x⊥y\}$

R is not reflexive as no line is perpendicular to itself

R is symmetric as if $(x,y)∈R⇒x⊥y⇒(y,x)∈R$

R is not transitive as if $(x,y)∈R$ & $(y,z)∈R$

$⇒x⊥y$ and $y⊥z$

so $x||z$ not $x⊥z$