Step 1: Determine the elements of relation R.

The relation R is defined by Ry if and only if y = max{x, 1}. We need to find all pairs (x, y) such that x ∈ A, y ∈ A, and y = max{x, 1}.

• If x = -2, y = max{-2, 1} = 1. So, (-2, 1) ∈ R.
• If x = -1, y = max{-1, 1} = 1. So, (-1, 1) ∈ R.
• If x = 0, y = max{0, 1} = 1. So, (0, 1) ∈ R.
• If x = 1, y = max{1, 1} = 1. So, (1, 1) ∈ R.
• If x = 2, y = max{2, 1} = 2. So, (2, 2) ∈ R.
• If x = 3, y = max{3, 1} = 3. So, (3, 3) ∈ R.

Therefore, R = {(-2, 1), (-1, 1), (0, 1), (1, 1), (2, 2), (3, 3)}.

Step 2: Find the number of elements in R (l).

The number of elements in R is l = 6.

Step 3: Determine the minimum number of elements to add to make R reflexive (m).

For R to be reflexive, it must contain (x, x) for all x ∈ A. A = {-2, -1, 0, 1, 2, 3}.

R already contains (1, 1), (2, 2), and (3, 3). We need to add (-2, -2), (-1, -1), and (0, 0) to make it reflexive.

So, m = 3.

Step 4: Determine the minimum number of elements to add to make R symmetric (n).

For R to be symmetric, if (x, y) ∈ R, then (y, x) ∈ R.

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

• (-2, 1) ∈ R, so we need (1, -2).
• (-1, 1) ∈ R, so we need (1, -1).
• (0, 1) ∈ R, so we need (1, 0).
• (1, 1) ∈ R, which is symmetric.
• (2, 2) ∈ R, which is symmetric.
• (3, 3) ∈ R, which is symmetric.

So, we need to add (1, -2), (1, -1), and (1, 0). Therefore, n = 3.

Step 5: Calculate l + m + n.

l + m + n = 6 + 3 + 3 = 12.