Internal direct product of proper subgroups

Question

Assignment:

Give an example of groups H_i, K_j such that H₁xH₂ is isomorphic to K₁xK₂ and no H_i is isomorphic to any K_j.

Let G be the additive group Q of rational numbers. Show that G is not the internal direct product of any two of its proper subgroups.

If G is the internal direct product of subgroups G₁ and G₂ show that G/G₁ is isomorphic to G₂ and G/G₂ is isomorphic to G₁.

Provide complete and step by step solution for the question and show calculations and use formulas.