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For a relation (R), what is the smallest symmetric relation that contains (R)?

Answer and explanation

Correct answer: (R\cup R^{-1})

Step 1: To make (R) symmetric, every pair needs its reverse. Step 2: (R^{-1}) provides exactly those reverse pairs, so (R\cup R^{-1}) contains all required pairs. Step 3: When the word smallest appears, reject options that add unnecessary pairs.

Related tags

Symmetric ClosureInverse RelationRelationsClass 12Symmetric RelationRelations And FunctionsMathematicsClass 12 Mcq

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