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+(y2−2)2≤4}
If the total number of relations from A∩B to A∩C is 2p, then the value of p is
A
16
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B
49
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C
25
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D
9
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Solution
The correct option is C25 The set A and B are represented as :
∴A∩B={(0,0),(1,0),(2,0),(1,1),(1,−1)}
The set A and set C are represented as:
∴A∩C={(1,1),(2,0),(2,1),(2,2),(3,2)}
Total number relations from A∩B to A∩C=25×5. ∴p=25