Relation and Function question bank (Maths)

For real numbers $x$ and $y$,we define the relation $R$ as $xRy$ if $x - y + \sqrt{2}$ is an irrational number. Then the relation $R$ is:

Let $R$ be a relation over the set $N \times N$ and it is defined by $(a, b)R(c, d) \iff a + d = b + c$. Then $R$ is