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On a family of sets, define (A R B) if (A \cap B=\varnothing). Is this relation transitive?

Answer and explanation

Correct answer: No

Step 1: Take (A={1}), (B={2}), and (C={1}). Step 2: (A \cap B=\varnothing) and (B \cap C=\varnothing), but (A \cap C={1}). Step 3: The disjointness relation is not necessarily transitive.

Related tags

Transitive RelationDisjoint SetsCounterexampleRelations And FunctionsMathematicsClass 12 Mcq

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