Which of the following statements is false?

If a perfectly competitive firm produces the quantity of output at which $MR=MC,$ it follows that the firm may or may not be earning a profit.

The firm's supply curve is that portion of its AVC curve that lies above its MC curve.

If price is above ATC at the quantity of output at which $MR=MC,$ the firm will be earning a profit.

In long$-$run competitive equilibrium, price is equal to marginal cost.