Let $R=\{(L_1,L_2): L_1 ⊥ L_2$ where $L_1, L_2 ∈L$ (set of straight line in a plane)$\}$, then
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → R is symmetric but neither reflexive nor transitive
$R = \{(L_1, L_2) : L_1 \perp L_2,\ L_1, L_2 \in L\}$
$\text{Reflexive: Not reflexive, since no line is perpendicular to itself} \text{ as There is no } L \in L \text{ such that } L \perp L$
$\text{Symmetric: Yes, because if } L_1 \perp L_2 \text{ then } L_2 \perp L_1$
$\text{Transitive: Not transitive, because } L_1 \perp L_2 \text{ and } L_2 \perp L_3 \text{ does not imply } L_1 \perp L_3$