problem: Determine the following statements are true or false?

[A]   An option can never sell for less than you can make by exercising the option.

[B]   A call option is always more valuable than a put option with the same strike price and the same maturity date on the same stock.

[C]   A call option with a higher strike price can never trade for more than a call option [on the same stock] with a lower strike price and the same maturity date.

[D]   Call options on stocks that do not pay dividends [until the options' maturity] will never be exercised early.

[E] As an option approaches expiration, its value will go down if the stock price does not change. (Assume that interest rates and the stock price variance do not change and dividends are not paid on the stock.)

[F]   An option [call or put] with less time to expiration will sell at a higher price than an option with more time to maturity. [Suppose that the options are on the same stock and have the same strike price.]

[G]   An option on a stock with higher variance will sell at a higher price than a similar option on a stock with lower variance.