The statement "The anaerobic conditions associated with rice cultivation cause the emission of methane" is correct. Methane is a potent greenhouse gas that contributes significantly to global warming. When rice paddies are flooded with water, anaerobic conditions are created in the soil. This encourages the growth of methane-producing microorganisms that release methane into the atmosphere. Therefore, rice cultivation is a significant source of methane emissions.

The statement "When nitrogen-based fertilizers are used, nitrous oxide is emitted from the cultivated soil" is also correct. Nitrous oxide is another potent greenhouse gas that contributes to global warming. When nitrogen fertilizers are applied to the soil, they are converted into nitrate, which can be easily leached from the soil. Nitrate that is not taken up by the plants can be converted into nitrous oxide through a process called denitrification. Nitrous oxide is then emitted into the atmosphere, where it can contribute to global warming.