Question

Let Z be the set of all integers,

A = {(x, y) ∈ Z × Z : (x – 2)² + y² ≤ 4},

B = {(x, y) ∈ Z × Z : x² + y² ≤ 4} and

C = {(x, y) ∈ Z × Z : (x – 2)² + (y – 2)² ≤ 4}

If the total number of relation from A ∩ B to A ∩ C is 2^p, then the value of p is :

(1) 16 

(2) 25 

(3) 49 

(4) 9

Answer 1

Option : (2). 25

(x – 2)² + y² ≤ 4

x² + y² ≤ 4

No. of points common in C₁ & C₂ is 5. 

(0, 0),(1, 0),(2, 0),(1, 1),(1, –1) 

Similarly in C₂ & C₃ is 5. 

No. of relations = 2^5×5 

= 2²⁵.