6.2.5 Binary relations

Problem: Let's consider on the set \( \mathbb{Z}^{2} \) the binary relation \( (k, l) \sim(m, n) \), which means that \( m+n-k-l \) is divisible by 3 . Is it an equivalence? Draw on checkered paper all such points \( (m, n), 0 \leq \) \( m, n \leq 10 \) that \( (m, n) \sim(0,0) \). Find the maximum number of pairwise incomparable points.