Problem on group homomorphism

Question

Assignment:

Let G₁ and G₂ be groups and φ:G₁→G₂ a map. Which of the following is a group homomorphism? Explain your answers. If φ is a homomorphism, describe the kernel and the image of φ.

G₁=C_4= , G₂=Z₂ (the integers modulo 2 with the operation +), φ:a^i?i (mod 2).
G₁=G₂=Z₅ (the integers modulo 5 with the operation +), φ:n?an(mod5) where a∈Z_5\{0}={1,2,3,4} is fixed.

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