The probability that a relation $R$ from $\{ x , y \}$ to $\{ x , y \}$ is both symmetric and transitive, is equal to

Let $M$ denotes set of all $3 \times 3$ non singular matrices. Define the relation $R$ by

$R = \{ (A,B) \in M \times M$ : $AB = BA\} ,$ then $R$ is-

$R$ is a relation over the set of real numbers and it is given by $nm \ge 0$. Then $R$ is

Let $R$ be a relation on the set $N$ be defined by $\{(x, y)| x, y \in N, 2x + y = 41\}$. Then $R$ is

 Solution set of $x \equiv 3$ (mod $7$), $p \in Z,$ is given by

Let $I$ be the set of positve integers. $R$ is a relation on the set $I$ given by $R =\left\{ {\left( {a,b} \right) \in I \times I\,|\,\,{{\log }_2}\left( {\frac{a}{b}} \right)} \right.$ is a non-negative integer$\}$, then $R$ is