Let `L` be the set of all lines in a plane and let `R` be a relation defined on`L` by the rule `(x,y)epsilonRtox` is perpendicular to `y`. Then prove that `R` is a symmetric relation on `L`.

Explanation

To prove that the relation \( R \) defined on the set of all lines \( L \) in a plane, where \( (x, y) \in R \) if and only if line \( x \) is perpendicular to line \( y \), is symmetric, we will follow these steps:

### Step 1: Understand the definition of a symmetric relation
A relation \( R \) is symmetric if for any two elements \( a \) and \( b \) in the set, whenever \( (a, b) \in R \), it must also be true that \( (b, a) \in R \).

**Hint:** Recall that for a relation to be symmetric, you need to show that if one condition holds, the reverse must also hold.

### Step 2: Assume \( (x, y) \in R \)
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