graph - self doubt

Question

Graph G has atleast 1 edge then which are true

a) G has a hamiltonian circuit

b) Every cycle of G is of even length

Comments

I think both options a and b dont have any relevancy with atleast one edge

since it simply means >=1 which could be anything so cant be deduced in best of my knowledge.

Answer 1

A) For Hamiltonian Circuit, there should be atleast 3 vertices, else how will we form a simple closed path ?
B) With 1 edge, cycle is  not possible. But with 3 edges cycle is possible, in that case it is a odd length cycle, not even

*Correct me if I am wrong