If dual problem is infeasible (feasible), is the primal problem infeasible/unbounded (feasible)?

Question

For a convex optimization problem, say $\cal P$, and its dual problem, say $\cal D$, is the following statement right?

If $\cal D$ is infeasible (feasible), then $\cal P$ is infeasible/unbounded (feasible).

Answer 1

Mathematical Programs can be unbounded or infeasible. Duality theory states that: If the primal is unbounded, then the dual is infeasible; If the dual is unbounded, then the primal is infeasible. But it's possible for both the dual and the primal to be infeasible.

Several papers are available on the internet where Duality theorems are discussed.