Let Z be the set of all integers, A = \ ( x, y ) ∈ Z × Z: ( x - 2 )...

$A = \left\{( x, y ) \in Z \times Z; ( x - 2{)}^{2} + {y}^{2} \le 4\right\}$

$B = \left\{( x, y ) \le Z \times Z; {x}^{2} + {y}^{2} \le 4\right\}$

$C = \left\{( x, y ) \in Z \times Z; ( x - 2{)}^{2} + ( y - 2{)}^{2} \le 4\right\}$

Here, we can see from the above diagram $A \cap B = { ( 0, 0 ) , ( 1, 0 ) , ( 2, 0 ) , ( 1, 1 ) , ( 1, - 1 ) } ⇒ n ( A \cap B ) = 5$

Similarly $n ( A \cap C ) = 5$

Relation from $A \cap B$ to $A \cap C = {2}^{5 \times 5} = {2}^{p}$

$⇒ p = 25$