For each of the following, draw a connected graph with no self$-$loops and has neither an Eulerian path nor an Eulerian circuit that satisfies the conditions.

a$)$ It is impossible to add an edge to make an Eulerian circuit or Eulerian path possible.

b$)$ No vertex has degree $1$ and it is impossible to remove an edge to make a graph with an Eulerian circuit or an Eulerian path, but it is possible to add an edge to produce a graph with an Eulerian circuit or an Eulerian path.