Draw the following relations as a subset of the plane:

1. The relation ~ on Z defined by, x ~ y if x ≡ y mod 4

2. The relation ~ on Z² defined by, (a, b) ~ (c,d) if there exists natural numbers m, n such that mb(b² - 3a²) = nd(d² - 3c²)

3. The relation ~ on ZxN defined by, (a, b) ~ (c, d) if ad = bc