Which of the following functions is symmetric, but neither reflexive nor transitive?

R = {(T1, T2): T1 is congruent to T2, where T is the set of triangles in a plane}

R = {(T1, T2): T1 is similar to T2, where T is the set of triangles in a plane}

R = {(L1, L2): L1 is parallel to L2, where L is the set of lines in a plane}

R = {(L1, L2): L1 is perpendicular to L2, where L is the set of lines in a plane}

Correct option is D

$\begin{aligned}&\textbf{Option 3:} \\[4pt]&R = \{(L_1, L_2) : L_1 \text{ is parallel to } L_2\}, \quad L = \text{set of lines in a plane} \\[6pt]&\bullet\ \textbf{Symmetric?} \ \text{Yes. If } L_1 \parallel L_2, \text{ then } L_2 \parallel L_1 \quad \text{\color{green}} \\&\bullet\ \textbf{Reflexive?} \ \text{Yes. Any line is parallel to itself.} \\&\bullet\ \textbf{Transitive?} \ \text{Yes. If } L_1 \parallel L_2 \text{ and } L_2 \parallel L_3, \text{ then } L_1 \parallel L_3 \quad \text{\color{green}} \\&\text{Again, symmetric, reflexive, and transitive} \\[10pt]&\textbf{Option 4:} \\[4pt]&R = \{(L_1, L_2) : L_1 \text{ is perpendicular to } L_2\}, \quad L = \text{set of lines in a plane} \\[6pt]&\bullet\ \textbf{Symmetric?} \ \text{Yes. If } L_1 \perp L_2, \text{ then } L_2 \perp L_1 \quad \text{\color{green}} \\&\bullet\ \textbf{Reflexive?} \ \text{No. A line is not perpendicular to itself} \quad \text{\color{red}} \\&\bullet\ \textbf{Transitive?} \ \text{No. If } L_1 \perp L_2 \text{ and } L_2 \perp L_3, \text{ then } L_1 \text{ is parallel to } L_3,\ \text{not perpendicular} \quad \text{\color{red}}\end{aligned}$