How does cooking vegetables deprive them of vitamins?

Cooking vegetables won't "deprive" them of vitamins since they will still have the vitamins after cooking. However, cooking will alter the vitamins' structures (heat denatures things like enzymes and proteins), which can then lower the bioavailability (the availability a nutrient has to be absorbed by the body) of the vitamins once you eat the cooked vegetable. The vitamins and nutrients are still present, but not to the extent they were when the vegetable was raw. To get maximum nutrients and vitamins from vegetables, eating raw or fresh-frozen (vegetables that are frozen at the peak of freshness - all the good stuff is still present) are the best. However, there are some important nutrients that become more bioavailable to the body after the cooking process (such as the antioxidant lycopene found in tomatoes).