Given a pair of primal-dual linear programming problems, P and D (min and max) in canonical form. Is part a true or false?

a) If a basic solution to the primal is infeasible and has an objective value less than the optimal value, then the associated complementary dual basic solution is feasible. - I think it is false because if the primal is infeasible then the dual is unbounded. Can I perhaps get a detailed explanation with a mathematical explanation?