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 show that the relation \( R \) defined on the set of all lines \( L \) in a plane is symmetric but neither reflexive nor transitive, we can follow these steps:

### Step 1: Define the Relation
Let \( L \) be the set of all lines in a plane. The relation \( R \) is defined as:
\[ R = \{(L_1, L_2) \in L \times L : L_1 \text{ is perpendicular to } L_2\} \]

...