Let $R = \{(a, a)\}$ be a relation on a set $A$. Then $R$ is

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

Let $R$ be a relation on $Z \times Z$ defined by$ (a, b)$$R(c, d)$ if and only if $ad - bc$ is divisible by $5$ . Then $\mathrm{R}$ is

Let $R =\{( P , Q ) \mid P$ and $Q$ are at the same distance from the origin $\}$ be a relation, then the equivalence class of $(1,-1)$ is the set

Consider set $A = \{1,2,3\}$ . Number of symmetric relations that can be defined on $A$ containing the ordered pair $(1,2)$ & $(2,1)$ is

Let $R$ be the relation on the set $R$ of all real numbers defined by $a \ R \ b$ if $|a - b| \le 1$. Then $R$ is