Mathematics - Sets and Relations Question with Solution | TestHub

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

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

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

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

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

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

$\Rightarrow p=25$