Consider the natural number x = ID2 + 4. Take the set Z, and the modulo x operations of addition + and multiplication ×. Is (Zx Xx) a monoid? Justify

your answer. Explain why (Zx+¤) is an abelian group. Does there exist a subgroup of (Zx +¤) which is isomorphic to (Z3, +3)? Justify your answer. O Prove that in any of the groups (Zp, +p) for some positive integer p, every element k with 0 < k < p has the same order as the group, if k and p are co-prime (are relatively prime to each other).[5]