Let L be the set of all lines in a plane and R be the relation in L defined as `R={(L_1,L_2):L_1`is perpendicular to `L_2`} Show that R is symmetric but neither reflexive nor transitive.

Explanation

To solve the problem, we need to analyze the relation \( R \) defined on the set \( L \) of all lines in a plane, where \( R = \{(L_1, L_2) : L_1 \text{ is perpendicular to } L_2\} \). We will show that \( R \) is symmetric but neither reflexive nor transitive.

### Step 1: Check for Reflexivity
A relation \( R \) is reflexive if every element is related to itself. In our case, we need to check if every line \( L_1 \) is perpendicular to itself.

- **Analysis**: A line cannot be perpendicular to itself because perpendicular lines meet at a right angle, and a line cannot intersect itself at a right angle.
- **Conclusion**: Therefore, \( R \) is **not reflexive**.

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