Which of the following statements is correct?

When there is no dividend payment prior to expiration, two otherwise identical call options, one European style and the other American style, might have different prices because the American call option owners have the right to$.$ exercise the option sooner than the European option owners.

When a put option is exercised, the payoff to the owner is equal to the exercise price minus the current stock price. When a call option on a share of stock is exercised, the payoff to the owner is equal to the current stock price $($S$)$ minus the exercise price $($X$).$ Thus, when the stock price is higher than the exercise price, the call option owner finds it profitable to exercise the option.

We are looking at an American put option and an American call option written on the same underlying asset, same exercise price and same time to expiration. When there is no dividend paid prior to expiration, the American put and American call should satisfy the put$-$call parity.

Because exercising an American put option will give you a value lower than keeping the option alive, it is usually not optimal for American put option owners to exercise it early.