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On integers, (aRb) if (a=b) or (a-b) is divisible by (5). Choose the correct option about transitivity of (R).

Answer and explanation

Correct answer: It is transitive

Step 1: The case (a=b) gives (a-b=0), and (0) is divisible by (5), so the relation is a same-remainder type condition. Step 2: If (a-b) and (b-c) are divisible by (5), then (a-c) is also divisible by (5). Step 3: Try to merge equality conditions with difference conditions when possible.

Related tags

Modulo 5Equality ConditionTransitiveTransitive RelationRelations And FunctionsMathematicsClass 12 Mcq

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