(a): We have, $A = \{(x,y)$ $\in Z \times Z:(x - 2)^{2} + y^{2} \leq 4\}$,\\ $B = \left\{ (x,y) \in Z \times Z:x^{2} + y^{2} \leq 4 \right\}$ and $C = \{(x,y) \in Z \times Z:(x - 2)^{2}$ $+ (y - 2)^{2} \leq 4\}$\\ Intersection of $A$ and $B$ is shown by graph as given. \end{enumerate} \includegraphics[width=3.11678in,height=2.13299in]{vertopal_a09d5a7ae2de483db956e76c708a9bbe/media/image4.jpg} So, $A \cap B = \{(0,0),(1,0),(2,0)$, $(1,1),(1, - 1)\}$\\ $\therefore\ n(A \cap B) = 5$ Also, intersection of $A$ and $C$ is shown by graph as given.\\ So, $A \cap C = \{(1,1),(2,0),(2,1)$, $(2,2),(3,1)\}$\\ $\Rightarrow n(A \cap C) = 5$ Number of relations from $(A \cap B)$ to $(A \cap C)$ \includegraphics[width=2.13129in,height=1.93121in]{vertopal_a09d5a7ae2de483db956e76c708a9bbe/media/image6.jpg} $= 2^{5 \times 5} = 2^{25} = 2^{p} \Rightarrow p = 25$ \begin{enumerate} \def\labelenumi{\arabic{enumi}.} \setcounter{enumi}{21}