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

Let $R$ be a relation over the set $N × N$ and it is defined by $(a,\,b)R(c,\,d) \Rightarrow a + d = b + c.$ Then $R$ 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 $I$ 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 

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 $N$

Determine whether each of the following relations are reflexive, symmetric and transitive :

Relation $\mathrm{R}$ in the set $\mathrm{A}=\{1,2,3, \ldots, 13,14\}$ defined as $\mathrm{R}=\{(x, y): 3 x-y=0\}$