Let Z, be the set of all integers,

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

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

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

If the total number of relations from A  $\cap$  B to A $\cap$  C is 2^p, then the value of p is:

Correct Option - 4


Detailed Solution:

number of elements in $A\cap B=5$ which is

(0, 0) (1, 0) (1, 1) (1, -1) (2, 0)

Similarly number of elements in $A\cap C=5$ which is

(2, 0) (2, 2) (1, 1) (2, 1) (3, 1)

Hence number of relation from

$\left(A\cap B\right)to\left(A\cap C\right)=2^{5\times 5}=2^{25}$            

->P = 25

 

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