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 + y 2 ≤ 4 } C = { ( x , y ) ∈ Z * Z : ( x − 2 ) 2 + ( y − 2 ) 2 ≤ 4 } If the total number of relations from A ∩ B to A ∩ C is 2p, then the value of p is:

number of elements in A ∩ B = 5 which is (0, 0) (1, 0) (1, 1) (1, -1) (2, 0) Similarly number of elements in A ∩ C = 5 which is (2, 0) (2, 2) (1, 1) (2, 1) (3, 1) Hence number of relation from (A∩B)to (A∩C)=25*5=225 ->P = 25

Let Z, be the set of all integers,

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

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

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

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

Option 1 - 49

Option 2 - 9

Option 3 - 16

Option 4 - 25

5 Views|Posted 6 months ago

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Answered by

Alok Kumar Singh | Contributor-Level 10

6 months ago

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

$(A \cap B) t o (A \cap C) = 2^{5 * 5} = 2^{25}$

->P = 25

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