Does Putting a Lid Over a Pot of Water on a Stove

Does putting a lid over a pot of water on a stove shorten the time it takes for the water to come to a boil? After the water is boiling, does use of the lid shorten the cooking time of food?

A) No, the boiling point of water is always 100°C, so the lid would have no effect on how long it takes for water to reach that temperature. however, food cooks faster with a lid because heat is held inside the pot.
B) Yes, since the pressure is increased under the lid the boiling temperature is lower; however, after the water boils, the increased pressure would prevent gas bubbles from escaping so the food cooks in about the same amount of time as without a lid.
C) Yes, the trapped heat quickens boiling; the lid also increases pressure on the boiling water which raises its boiling temperature, cooking food in a shorter time.
D) No, it takes longer to boil the water because the increased pressure in the pot raises water's boiling point. Food will cook faster because the temperature of the water is higher.