Determine whether Relation `R` on the set `A={1,\ 2,\ 3,\ ,\ 13 ,\ 14}` defined as `R={(x ,\ y):3x-y=0}` is reflexive, symmetric or transitive.

Explanation

To determine whether the relation \( R \) on the set \( A = \{1, 2, 3, \ldots, 14\} \) defined by \( R = \{(x, y) : 3x - y = 0\} \) is reflexive, symmetric, or transitive, we will follow these steps:

### Step 1: Determine the relation \( R \)

We need to find all ordered pairs \( (x, y) \) such that \( 3x - y = 0 \) for \( x \) in the set \( A \).

1. Rearranging the equation gives us \( y = 3x \).
2. Now we will substitute values of \( x \) from the set \( A \) and find corresponding \( y \):
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