QPaperGen

We are given:
\[
x R y \;\;\Leftrightarrow\;\; 2x - y \in \{0,1\}.
\]

Thus,
\[
y = 2x \quad \text{or} \quad y = 2x - 1.
\]

For \(A = \{-3,-2,-1,0,1,2,3\}\), we list all possible pairs:

\[
R = \{(-1,-2),(0,0),(1,2),(-1,-3),(0,-1),(1,1),(2,3)\}.
\]

Hence,
\[
l = |R| = 7.
\]

\[ \textbf{Reflexivity:}\]
For reflexivity, we need \((a,a) \in R\) for all \(a \in A\).

But the rule requires \(2a - a = a \in \{0,1\}\), so only \((0,0)\) and \((1,1)\) are present.

The remaining \(5\) pairs \((a,a)\) for \(a \in \{-3,-2,-1,2,3\}\) are missing.
Thus, \(m = 5\) must be added.

\[ \textbf{Symmerty:}\]
A relation is symmetric if \((x,y) \in R \Rightarrow (y,x) \in R\).

Currently, the following pairs are missing:
\[
(-1,-2) \Rightarrow (-2,-1), \quad
(1,2) \Rightarrow (2,1), \quad
(-1,-3) \Rightarrow (-3,-1), \quad
(0,-1) \Rightarrow (-1,0), \quad
(2,3) \Rightarrow (3,2).
\]

So \(n = 5\) pairs must be added.

Final Count
\[
l + m + n = 7 + 5 + 5 = 17.
\]

\[
\therefore \quad \text{Correct Answer is (A) 17.}
\]