Equivalence Relation & Equivalence Class

If $N$ denotes the set of all natural numbers and $R$ be the relation on $N\times N$ defined by $\left(a,b\right) R\left(c,d\right)$ and if $ad\left(b+c\right)=bc\left(a+d\right)$, then $R$ is

$x^2=xy$ is a relation which is

In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation, it is sufficient, if $R$

Let $R$ be a relation on a set $A$ such that $R=R^{-1},$ then $R$ is

Let $P\mathit{=}\left\{\left(x\mathit{,}\mathit{ }y\right)\mid x^2+y^2=1\mathit{,}x\mathit{,}y\mathit{\in }R\right\}$. Then, $P$ is