Mathematics · Group Theory

Given below are two statements: Statement (I): If H is a non-empty finite subset of a group G and ab ∈ H ∀ a, b ∈ H, then H is also a group under the same operation. Statement (II): There is no homomorphism that exists from (Z, +) to (Q, +); where Z is the set of integers and Q is the set of rational numbers. In the light of the above statements, choose the most appropriate answer from the options given below: