Let $R$ be a relation on the set $N$ of natural numbers defined by $nRm $$\Leftrightarrow$ $n$ is a factor of $m$ (i.e.,$ n|m$). Then $R$ is

Let $R$ and $S$ be two non-void relations on a set $A$. Which of the following statements is false

Show that the relation $R$ defined in the set A of all triangles as $R =\left\{\left( T _{1},\, T _{2}\right):\, T _{1}\right.$ is similar to $\left. T _{2}\right\}$, is equivalence relation. Consider three right angle triangles $T _{1}$ with sides $3,\,4,\,5, \,T _{2}$ with sides $5,\,12\,,13 $ and $T _{3}$ with sides $6,\,8,\,10 .$ Which triangles among $T _{1},\, T _{2}$ and $T _{3}$ are related?

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

If $R$ is a relation on the set $N$, defined by $\left\{ {\left( {x,y} \right);3x + 3y = 10} \right\}$

Statement $-1$ : $R$ is symmetric

Statement $-2$ : $R$ is reflexive

Statement $-3$ : $R$ is transitive, then thecorrect sequence of given statements is

(where $T$ means true and $F$ means false)

Let $A=\{1,2,3,4\}$ and $R$ be a relation on the set $A \times A$ defined by $R=\{((a, b),(c, d)): 2 a+3 b=4 c+5 d\}$. Then the number of elements in $R$ is: