Let Z be the set of all integers, [A = (x,y) Z Z:(x - 2)^2 + y^2 4 ] [B = (x,y) Z Z:x^2 + …

Question

Let Z be the set of all integers,

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

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

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

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

Accepted Answer

(x - 2)2 + y2 $$\le$$ 4

x2 + y2 $$\le$$ 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$$ 5 \times 5$$ = 225.

Solutions · 1