Determine whether the following relation are reflexive, symmetric and transitive relation $\mathrm{R}$ in the set $\mathrm{A}=\{1,2,3,\dots ,10\}$ defined by $\mathrm{R}=\left\{\right(x,y):2x-y=0\}$.

Determine whether each of the following relations are reflexive, symmetric and transitive relation $\mathrm{R}$ in the set $Z$ of all integers defined by $\mathrm{R}=\left\{\right(x,y):x-y \mathrm{is} \mathrm{an} \mathrm{integer}\}$.

Determine whether each of the following relations in the set $A$ of human beings in a city at a particular time are reflexive, symmetric and transitive: $R=\left\{(x,y):x \mathrm{and} y\right\}$ work at the same place.$$

Determine whether each of the following relations in the set $A$ of human beings in a city at a particular time are reflexive, symmetric and transitive:$R=\left\{\right(x,y):x\text{ and }y$   work at the same locality }.