Without (the / no article) air and water, living things could not survive

Question

Could you please advise whether I should use definite article 'the' in the below sentence?

I'm helping my little sister with an exercise of filling suitable article(s) into the blank of the sentence:

Without ______ (a / an / the / no article) ____ air and water, living things could not survive.

My sister and I both agree that we don't use indefinite articles 'a' or 'an' before uncountable nouns like 'air' and 'water'. However, we have different views about the use of 'the' or 'no article' in this sentence.

For me, no article is needed in the sentence because

Rule #3 - All things or things in general: Use no article with plural count nouns or any noncount nouns used to mean all or in general.
[...]
Noncount nouns are those which usually cannot be counted. Following are some common examples:
[...]
- Certain food and drink items: [...] sugar, tea, water, wine, yogurt
- Certain nonfood substances: air, cement, coal, dirt, [...]
Source: https://www.butte.edu/departments/cas/tipsheets/grammar/articles.html

I showed her some example sentences:

Without air there is no sound.
Source: https://science.nasa.gov/science-news/science-at-nasa/2013/01nov_ismsounds

How many days can a human survive without water?
Source: http://www.businessinsider.com/how-many-days-can-you-survive-without-water-2014-5

However, my sister thinks 'the' is needed in the sentence because

The definite article is used in front of things generally regarded as unique: The sun, the moon, the sea, the sky, the Arctic Circle, the environment, the capital, the air, the ground, etc.
Source: http://www.davidappleyard.com/english/articles.htm

and she found some examples as well:

Birds and insects could not fly without the air to support them. Without the air, humans would not be able to fly either.
Source: http://www.scienceterrific.com/atmosphere_function.php

We can’t survive for more than a few minutes without the air, so why isn’t the air as much a part of us as our legs or arms?
Source: http://reasonandmeaning.com/category/anxiety-depression/

To put into more simpler terms, if your body is dehydrated and you have just finished a tough gym session and have eaten a protein rich meal – without the water the protein will never get to the muscles and therefore never get repaired.
Source: http://www.home2officewatercoolers.co.uk/why-its-vital-for-your-health-to-drink-water-at-work/

Answer 1

I can see you've done a lot of research, and have come up with an ambiguous understanding which is a shame (English sucks). I hope I can help clear the air for you. :)

Your first instinct about there being no article needed in the first example was correct:

Without air and water, living things could not survive.

In fact, in most of the examples your sister found to support the being the correct particle, the could actually be removed entirely:

Birds and insects could not fly without air to support them. Without air, humans would not be able to fly either.

We can’t survive for more than a few minutes without air, so why isn’t air as much a part of us as our legs or arms?

To put into more simpler terms, if your body is dehydrated and you have just finished a tough gym session and have eaten a protein rich meal – without water the protein will never get to the muscles and therefore never get repaired.

In all of the examples above, "air" is being referred to more as a concept than as a tangible thing. We're not talking about a "specific air" that we could hold or touch or see. Also, it's not just a concept of one thing, but "some amount" of it. The sentences above aren't referring to one air, but rather an amount of air. However, like you said, it is uncountable, neither plural nor singular. I'll try replacing the word air with information. Again, we're not referring to any specific information, but rather the concept of some amount of information. I know, it's silly, and doesn't make sense...but it works, grammatically:

Birds and insects could not fly without information to support them. Without information, humans would not be able to fly either.

We can’t survive for more than a few minutes without information, so why isn't information as much a part of us as our legs or arms?

To put into more simpler terms, if your body is dehydrated and you have just finished a tough gym session and have eaten a protein rich meal – without information the protein will never get to the muscles and therefore never get repaired.

See? It works, even if it's nonsense.

In this example, things are a little different:

The sun, the moon, the sea, the sky, the Arctic Circle, the environment, the capital, the air, the ground, etc.

The reasoning is correct, that "the definite article is used in front of things generally regarded as unique." There is only one air being referred to here: the air on Earth.

So to sum up, think of the first example again. Is the sentence referring to an amount of non-specific air? Yes. So, we don't need to use the.

Answer 2

Both are correct, but in your example standard American use would NOT include an article: Without air and water, living things could not survive.