Is cereal supposed to be cooked?

Packaged cereal such as corn flakes, raisin bran, or the Toasty O's in your picture is "ready-to-eat" — you can eat it dry, right out of the box if you wish, although many people enjoy adding some kind of milk (cows milk, soy milk, almond milk, etc.).

I don't think it would taste very good just mushed up with water. If that's all I had, I'd eat the cereal dry and drink the water separately — you can easily try it yourself and see what appeals to you.

Other cereals like oatmeal and wheat farina usually taste better when cooked, though you could eat dry oatmeal if you wanted.

There are a few main reasons people generally eat cereal with milk:

• Without any liquid, cereal would be pretty dry and hard to eat a lot of - you'd end up really wanting something to drink.
• Adding liquid also softens the cereal, not enough to make it totally soggy, but enough to lessen the crunch a little bit and make it more pleasant to chew.
• Milk has flavor, and people like that combination.
• Unless you're using skim milk, the fat in the milk changes the mouthfeel a bit, and people like that too.
• People are used to it. In the US at least, most everyone has been eating cereal with milk since they were a kid.

None of that is anything to do with cooking! You use cold milk, and eat it right away before it gets soggy. Depending on the cereal, by the time you finish the bowl, it might already be more soggy than you like. It doesn't need cooking.

So, you certainly could eat cereal with cool/cold water if you wanted to. Most people would probably find it pretty bland, but it might be better than trying to eat a ton of it dry. Alternatively, just eat it dry as a snack; you'll probably eat less of it, and more slowly, but it'll still taste good, and you can drink some water when your mouth gets too dry.

You definitely don't want to use hot water or actually boil it with this kind of cereal, though. You'll end up with an awful mess of disintegrated cereal. Same goes for anything else in a rectangular box from the cereal aisle like the one you have.

If you want a hot, cooked cereal, you need something like oatmeal or cream of wheat that has enough texture and substance to survive that. Anything meant to be cooked will have instructions on the package for cooking it.

A final note: all of that was based on you not having milk, as you said in the question. But if you hadn't said that, by far my first recommendation would've been to just get some milk. Milk and cereal is great.

With cold breakfast cereals the milk isn't meant to "melt" the cereal. Ideally the cereal is consumed before it gets soggy, while the cereal is still crunchy. The milk is just added to provide flavour and nutrition, adding water would do neither. If you don't have any milk I'd recommend just eating these sorts of breakfast cereals plain with anything added. They can make for a nice snack this way, though I wouldn't want to have plain cereal regularly for breakfast.