Number of binary operations on the set $\left\{a,b\right\}$ are

Determine whether the following relation is reflexive, symmetric and transitive: Relation $R$ in the set $A=\{1,2,3,...,13,14\}$ defined as $R=\{\left(x,y\right):3x–y=0\}$.

Determine whether the given relation is reflexive, symmetric and transitive: Relation $R$ in the set $N$ of natural numbers defined as $R=\left\{\right(x,y):y=x+5$ and $x<4\}$.

Determine whether the given relation is reflexive, symmetric and transitive: Relation R in the set $A=\{1,2,3,4,5,6\}$ as $R=\left\{\right(x,y):y$ is divisible by $x\}$.

Determine whether the given relation is reflexive, symmetric and transitive: Relation $R$ in the set $Z$ of all integers defined as
$R=\left\{\right(x,y):x–y$ is an integer $\}$.

Determine whether the given relation is reflective, symmetric and transitive$:$ Relations $R$ in the set $\mathrm{A}$ of human beings in a town at a particular time given by $R=\left\{\right(x,y):x$ and $y$ live in the same locality $\}$.

Determine whether the given relation is reflexive, symmetric and transitive$:$ Relations $R$ in the set $A$ of human beings in a town at a particular time given by $R=\left\{\right(x,y):x$ is exactly $7 \mathrm{c}\mathrm{m}$ taller than $y\}$.

Determine whether the given relation is reflexive, symmetric and transitive$:$ Relation $R$ in the set $\mathrm{A}$ of human beings in a town at a particular time given by $R=\left\{\right(x,y):x$ is wife of $y\}$.