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:
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Player 2
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L
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R
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Player 1
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A
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4, 0
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0, 3
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B
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0, 3
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2.5, 0
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C
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1, 1
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1, 1
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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.