A "properly mixed strategy" means a mixed strategy that does not assign all the probability to one pure strategy. In other words, it is not a pure strategy. Consider a simultaneous move game with the following payoff matrix:

a) Is pure strategy C strictly dominated by any other pure strategy of player 1? If so, write one out. If not, explain.

b) Is pure strategy C strictly dominated by any proper mixed strategy for player 1? If so, write one out.  If not, explain.

c) Is pure strategy C a best response to some mixed strategy of player 2? If so, write one out. If not, explain.