Vaporization and Condensation - College Chemistry

For this question, we're told that water is boiling and that the pressure above the surface of the water increases. We're asked to find out what will happen to the water.

It's important to remember the definition of a boiling liquid; the vapor pressure of the liquid is equal to the atmospheric pressure above the solution. Thus, if the atmospheric pressure increases, the vapor pressure would then become lower than the atmospheric pressure. As a result, the water would cease to boil. Moreover, its boiling point would increase because a higher temperature would be necessary in order to raise the vapor pressure enough so that it becomes equal to atmospheric pressure.