Solution

The correct answer is Statement I is correct but Statement II is incorrect 

EXPLANATION:

• 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.
  • This statement is correct under the condition that H also contains the identity element of G and that for each element in H, its inverse is also in H. These are key requirements to being a subgroup and therefore a group on its own.
• Statement (II): There is no homomorphism exist from (Z, +) to (Q, +), where Z is the set of integers and Q is the set of rational numbers.
  • This statement is false. A homomorphism does exist from (Z, +) to (Q, +). One such example could be the identity function f(x) = x where both addition operations remain preserved.

So, the answer would be Statement I is correct but Statement II is incorrect