True or false? the perfectly competitive firm should always produce the output level for which price equals marginal cost. explain your reasoning

Yes i think that statement true.

In the perfectly competitive firm, there is no distinction that may cause a customer to choose one seller over another.
Under that condition, eventually the sellers will have to control the output level to be equal with marginal cost. If they produce less, they won't maximize their profit, if they produce more they will have inventory surplus.