On the set R of real numbers, the relation $$\rho $$ is defined by x$$\rho $$y, (x, y) $$ \in $$ R.

Let $$\rho $$ be a relation defined on N, the set of natural numbers, as

$$\rho $$ = {(x, y) $$ \in $$ N $$ \times $$ N : 2x + y = 41}. Then

On the set R of real numbers we define xPy if and only if xy $$ \ge $$ 0. Then, the relation P is

On R, the relation $$\rho$$ be defined by 'x$$\rho$$y holds if and only if x $$-$$ y is zero or irrational'. Then,