ZXZ Q7) What theorem have you verified here? Can you see that Z? Z Q8) Find a new map such that the old map addition becomes a ring homomorphism. Q9) Now +: N x N N does not give a natural map. Why? Q10) After discussion with my student Priyadarshini, I decided to include this question. Can you find addition map(s) which is a vector space homomorphism. Q11) Describe the verified theorem geometrically. Q12) Check whether the maps f: ZxZ Z defined by f((a, b)) = ma + nb, m, ne Z are group homomorphisms. Ac