Repeating determiners: “the X and (the) Y”

I have a problem with the use of "the" after "and" where you would basically be connecting words. For example, which of the following is better:

The table and the chairs?
The table and chairs?

Or are both okay? What is the rule, and are there exceptions to it? Or is the rule just contextual and may vary between the sentences and meanings?

The is a determiner, which is, as described by Wikipedia:

a word, phrase or affix that occurs together with a noun or noun phrase and serves to express the reference of that noun or noun phrase in the context. That is, a determiner may indicate whether the noun is referring to a definite or indefinite element of a class, to a closer or more distant element, to an element belonging to a specified person or thing, to a particular number or quantity, etc. Common kinds of determiners include definite and indefinite articles (like the English the and a or an), demonstratives (this and that), possessive determiners (my and their), and quantifiers (many, few and several).

It is important to note that determiners modify (or, well, determine) noun phrases, which means that they don’t necessarily determine just a noun and nothing else. The entire noun phrase is under the scope of the determiner; for example:

The [big black Chevrolet that just passed by on the other side of the street]

Here, the determines not just Chevrolet, but everything inside the square brackets. A noun phrase, as you can see, can have various other things embedded into it, such as a relative clause and a locative phrase in the example above.

It can also consist of several noun phrases joined by a coordinator like and; for example:

My [mum and dad] live in Antarctica

Here, both mum and dad are clearly part of the same noun phrase, both being governed by my. If you switched the order of the two, you wouldn’t get dad and my mum, but my dad and mum.

But of course, and, being a general coordinator, can also coordinate entire noun phrases. It depends entirely on the context and the intended meaning whether an and coordinates two noun phrases inside a single noun phrase, or two main noun phrases. Very simply put: if it’s the former, then the entire thing is closely connected and perceived as a single ‘thing’: one unit. If it’s the latter, then it’s two distinct things.

In your case, there is no way to know whether table and chairs are to be seen as being closely related, effectively a single semantic unit, or whether they’re seen as separate entities that just happen to be put next to each other in the sentence.

Edwin’s first example is a good one that makes the difference clear:

The [table and chairs] cost £300.
The [table] and the [chairs] cost £300.

The first is quite clear: £300 is the total price you pay for both the table and the chairs that go with it.

The second is less so: it may mean the same, but it may also mean that the table costs £300, and the chairs cost £300 too.

This ambiguity is because even when you split something up into two distinct noun phrases, the following verb can still easily apply to both of them as one; or it can apply to them separately. This is an ambiguity you’ll just have to live with.

There is much less space for a verb to apply separately to two noun phrases if they’re embedded into a single noun phrase, which is why no one would naturally think that the total price in the first sentence was £600.

Even so, the longer each noun phrase gets, the more likely we are to separate them out as distinct noun phrases, rather than having one determiner govern over both of them—determiners are short little words, and they can have trouble governing too much.

The first is the plainest meaning, but conjunction reduction is very common in normal speech and writing. Generally we omit repeated articles, especially if the two things joined by the and are relatively short: We're more likely to leave in the the if it was "the early-twentieth century table made from a solid piece of imported South-East Asian mahogany and the four fake Arne Jacobsen chairs of the sort Christine Keeler sat on in the famous photograph" than we are in "the table and the chairs".

With single words or short phrases, choosing to include the second the causes a noticeable repetition, which causes the two elements (in this case tables and chairs) to be emphasised as individual elements rather than lumped into one unit.

Of course, in either case they are both separate elements and lumped into one unit; it's a matter of emphasis more than of meaning.