This is quite a basic question.
freedom is an abstract noun: Freedom is good. Freedom of speech is even better.
In English, abstract nouns do not take articles:
Wealth is a relative concept.
Freedom has many tentacles. Freedom of movement was restricted in that year.
Love has many splendors.
This includes adding something to the abstract noun with an of:...
1. You have egg on your tie.
Without an article, egg is being used as a mass noun. It's quantifiable, but not countable.
It's effectively the same as saying:
You have some amount of egg on your tie.
It could be a teaspoon worth of egg material or a cup worth. (Or any other measure.)
2. You have (an / the) egg on your tie.
This means that you have a ...
Interestingly, the cited example is one where usage has changed significantly over the last century...
(It's the same when restricted to AmE or BrE corpus, so it looks like a global phenomenon.)
Personally, I don't think it's particularly meaningful to attach any actual significance to the inclusion of the article, since it seems inconceivable that the ...
I do not know the technical reason for this difference but maybe I can shed some light on why we use the vs. a in that context.
If one were to say, "I am going to a hairdresser" it typically implies that they (the person saying it) have not yet determined which hairdresser they are going to; they could be going to any hairdresser. If they say "I am going to ...
If X is a stand-in for an actual, named algorithm, then X Algorithm is usually the correct construction. For example:
The A* algorithm
The DFS shortest path algorithm
The wikipedia page you cite isn't using "Algorithm A" to mean the same thing as "A* algorithm." It's using "Algorithm A" as shorthand for "Any algorithm, which we will ...
Property can be a count noun, but in this sense it is not, so as a property doesn't make sense.
You could say
He treats his dog as property.
but it is much more natural to say
He treats his dog as his property.
I think you have two non-dependent issues, which is where the confusion may come from:
Is there only one generic function or are there more than one possible functions from which to choose? If there is only one, use the definite article - "the generic function". If there are a few to choose from, use "a generic function." or "the most appropriate generic ...
When you use the definite article the it should be to single something out as specific among similar peers. The car, for example, would be a specific car - perhaps your car - and it singles it out from among other cars.
When you are talking about something being the best, it is, therefore, being singled out as such from among other things.
You can say that ...
(1) means one scarf of two colours.
(2) and (4) are wrong: we can't say a scarves.
(3) is correct, if a bit formal.
I think most English speakers would say "I see a green scarf and an orange one", but that's the same number of words.
The speaker/writer believes the question "which freedom?" matters. Here's how it could matter. The subtle subtext in this sentence is that the wheelchair restores 1 freedom--and which freedom is that? it's the freedom "to go out on his own". But other freedoms are not restored, such as the freedom to walk.
Definite articles are sometimes use to subtly ...
Newspaper headlines often use this telegraphic and strictly speaking ungrammatical convention.
From back in the days of typesetting with molten lead, they want to squeeze in as many content words as possible into a small space.
It is not a mistake to say "a subscription" but it is not normally what you mean.
The first example looks wrong to me. The word "subscription" should be used a countable noun, and so you need some article or determiner.
The second is correct. If a person had multiple subscriptions and the meaning was "you can cancel one of them". However this is ...
(1) refers to a conference as an organised event - "International Conference on XYZ"
(2) refers to Mr Dickson being one of a group of people conferring together; it might be part of a larger event, or just a situation where local officials have come together to discuss some serious issue that has arisen.
For the most part, the meaning stays the same, with or without the.
The meaning of "people in America are politically aware" is: *the majority of people in America are politically aware" or "all typical Americans are politically aware."
The literal meaning of "the people in America are politically aware" is: all of the people in America are politically ...
This is an effort to summarize the comments thus far, with a bit of my own editorializing.
Some of your examples can be explained by the relationship of articles to proper-noun geographic terms. We would never say something like “I traveled to the Africa” or “I am from the England,” because Africa and England are the names of places, and the names of places ...
The definite article (the) is used to indicate that the identity of the noun is known to the reader. The indefinite article (a) is used when its identity is not known.
So it all comes down to whether or not your audience has heard of "New York", or "a table" before.
I can't imagine anyone not knowing what a table is, but let's assume you're introducing a ...
The question is not well asked.
There are two meanings of "country". One is "State" the other is "countryside". Both reading are possible. There is no need to say "foreign country" or similar, though this can prevent ambiguity
In the first sense you would probably use "a", and so no correction is needed.
In the second sense you would probably use "the" ...
Well, you could deliberately construct a context where the version with the definite article works:
There are two boxes in the room. This box (pointing to one) is big. This is the big box.
However, I would advise against making up more context to fit with an otherwise incorrect answer. Since in your title you specify the test as from a textbook for ...
I think this is simply an idiom, a less formal way of saying "We are starting the class now."
"We are starting class now." assumes that the people now which specific class ('the' definite article) is being described.
I think it is more commonly used in American english than UK english.
To me, I think you need "The" definite article on the front of the first two, as you are speaking about 'the' performance specific to or of thread-related features and applications.
I don't see any risk of ambiguity, even though you are speaking generically and not specifying any one or a specific number of thread-related features or applications. As I ...
Definite noun phrases have different uses in English. A general usage is that the speaker uses a definite noun phrase when they assume that the hearer can identify the referent of the noun phrase.
I like the movie, Pulp Fiction.
The speaker assumes the hearer can identify the referent, that is, the hearer can identity which movie the speaker ...
Is that a rule that I always have to put an article before countable nouns
When the noun is not a proper noun, and referring to something that, in that sentence, can be counted, then yes.
If you can answer the question which X sensibly, then X is countable.
On Horse Market
Proper nouns in English are capitalized. You don't use an article here because ...