Crunchier veggie = more nutrients?!
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Vegetables start losing nutrients from the moment they are picked. And as seriousb said, cooking unocks certain nutrients, making them easier to absorb. The easiest way to cook vegetables and retain nutrients is steaming or microwaving in as little water as possible. Boiling vegetables in water leaches out some of the nutrients.
But on the broad scale of things, unless the vegtables are cooked to mush, they will be fine.
The point about losing nutrients in water has to do with the fact that you're throwing the water away. If you were making soup, then it wouldn't matter. If you're sauteing, you don't have that water for the nutrients to leach into and when tiny bits of moisture leach out of the vegetables, some of that ends up clinging to the vegetables as they cook. It's the water that's evaporating, and it's not necessarily taking all the good stuff with it.
Seriously, though, I doubt there's ever a point where all the nutrients completely disappear. If that was the case, people who live on canned foods would be walking around with all sorts of deficiency diseases.
You're probably best off with a combination of cooked and raw foods, and with a variety of cooking methods. That way you're getting all the possibilities (and exposing your child to all sorts of flavors and textures), because as was said above, some nutrients are released by cooking while others are destroyed. If the diet is varied enough, you've got all the bases covered.
A normal diet provides more than we need to stay healthy so there's no need to stress too much about the details, unless there's some medical reason to do so. Consider how many people are getting their servings of fresh vegetables on their fast food burgers or how many parents say that their kids eat nothing but nuggets, fries and ketchup. And there are all sorts of people on crazy restricted diets, too, and for the most part, the problem is not what they're missing in the diet, but what they're getting too much of.
Of course you want to do better than that but at some point it's just overkill to stress about losing a nutrient when the carrots are overcooked, because you're probably providing more nutrients than are needed. And if you still aren't sure you're doing the right thing, there are all sort of vitamin supplements that will fill in the gaps.
If you need to cook things until they are really soft, then soups are an option. That way you're keeping the cooking liquid.
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