Let $R$ be a relation on the set $A$ of ordered pairs of positive integers defined by $(x, y) R (u, v)$ if and only if $x v=y u .$ Show that $R$ is an equivalence relation.

Let $R_1$ be a relation defined by $R_1 =\{(a, b) | a \geq b, a, b \in R\}$ . Then $R_1$ is

If $n(A) = m$, then total number of reflexive relations that can be defined on $A$ is-

Let $A=\{1,2,3\} .$ Then number of relations containing $(1,2)$ and $(1,3)$ which are reflexive and symmetric but not transitive is

Let $R _{1}=\{( a , b ) \in N \times N 😐 a – b | \leq 13\}$ and $R _{2}=\{( a , b ) \in N \times N 😐 a – b | \neq 13\} .$ Thenon $N$