Given any element $a$ in $A$, both $a$ and $a$ must be either odd or even, so that $(a, a) \in R$ Further, $(a, \,b) \in R $ $\Rightarrow$ both $a$ and $b$ must be either odd or even $\Rightarrow(b, a) \in$ $R$ similarly, $(a,\, b) \in R$ and $(b,\, c) \in R$ $\Rightarrow$ all elements $a, \,b,\, c,$ must be either even or odd simultaneously $\Rightarrow(a, \,c) \in R$. Hence, $R$ is an equivalence relation. Further, all the elements of $\{1,3,5,7\}$ are related to each other, as all the elements of this subset are odd. Similarly, all the elements of the subset $ \{2,4,6\} $ are related to each other, as all of them are even. Also, no element of the subset $\{1,3,5,7\}$ can be related to any element of  $\{2,4,6\}$ , as elements of $\{1,3,5,7\}$ are odd, while elements of  $\{2,4,6\}$ are even.