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2 months ago

Relations Class 11th

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:
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A
alok kumar singh

Contributor-Level 10

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

 

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