Given below are two statements: Statement I: If S is a non-empty finite subset of a group K and for every x, y ∈ S, the product xy ∈ S, then S is a subgroup of K. Statement II: There exists no homomorphism from the group of real numbers (&mathbb;R, +) to the group of rational numbers (&mathbb;Q, +). In the light of the above statements, choose the most appropriate answer from the options given below:

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Mathematics · Group Theory

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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Correct answer

Statement I is correct but Statement II is incorrect

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Answer 1

Both Statement I and Statement II are correct

Answer 2

Both Statement I and Statement II are incorrect

Answer 3

Statement I is correct but Statement II is incorrect

Answer 4

Statement I is incorrect but Statement II is correct

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