# If a primal LP is infeasible, is it's dual LP always feasible?

I'm struggling with this question. I understand that with the strong duality theorem, the dual LP is infeasible when primal is unbounded (ex: linear programming infeasibility, dual & primal relation).

My intuition tells me this is false, but I'm having trouble coming up with an example to prove it. Any pointers?

Consider the linear programming problem of $$\min c^Tx$$ subject to $$Ax=b.$$
where $$A=0, c=b=1$$ and $$x \in \mathbb{R}$$.