Question

Let $Z$ be the set of all integers,
$A=\left\{(x,y)\in Z\times Z:(x-2{)}^2+y^2\le 4\right\}$
$B=\left\{(x,y)\in Z\times Z:x^2+y^2\le 4\right\}$ and
$C=\left\{(x,y)\in Z\times Z:(x-2{)}^2+(y-2{)}^2\le 4\right\}$
If the total number of relation from $A\cap B$ to $A\cap C$ is $2^p$, then the value of $p$ is :

• A. 16
• B. 25
• C. 49
• D. 9

Answer 1

Answer: (B)

$(x-2{)}^2+y^2\le 4$
$x^2+y^2\le 4$
No. of points common in $C_1\&C_2$ is 5 .
$(0,0),(1,0),(2,0),(1,1),(1,-1)$
Similarly in $C_2\&C_3$ is 5 .
No. of relations $=2^{5\times 5}=2^{25}$.