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On positive integers, (aRb) if and only if (a) and (b) have the same power of (2), that is, (a=2^k m) and (b=2^k n), where (m,n) are odd. What forms the equivalence class of (12)?

Answer and explanation

Correct answer: Numbers having exactly power (2) of (2)

Step 1: (12=2^2\cdot 3), so it has exactly power (2) of (2). Step 2: The relation checks only this power of (2). Step 3: Hence the class contains numbers divisible by (4) but not by (8).

Related tags

Power Of 2Positive IntegersEquivalence ClassNumber TheoryEquivalence RelationRelations And FunctionsMathematicsClass 12 Mcq

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