Compute the indicated quantities for the given homomorphism¢. 

Ker(∅) and ∅(3, 10) for ∅: Z x Z → S₁₀ where ∅(1, 0) = (3, 5)(2, 4) and ∅(0, 1) = (1, 7)(6, 10, 8, 9)

Data  from Exercise 46

Let a group G be generated by {a_i | i ∈ I}, where I is some indexing set and a_i ∈ G for all i ∈ I. Let ∅ : G → G' and µ : G → G' be two homomorphisms from G into a group G', such that ∅(a_i) = µ(a_i) for every i ∈ I. Prove that ∅ = µ. [Thus, for example, a homomorphism of a cyclic group is completely determined by its value on a generator of the group.]