Which best fits this sentence?
For conferencing to happen, internet connection is _________.
- a mandatory
When I try to search, I found both of them in use and I got confused.
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The sentence "X is Y", where X is a noun and Y is an adjective, is an unexceptional sentence. "Jim is old", "cats are friendly", "attendance is mandatory."
The sentence "X is a Y", where X is a noun and Y is an adjective, implies the adjective has been promoted to a noun for some reason.
Almost any adjective can be promoted to a noun, but fairly few ever are. For example, if you said, "Jim is deplorable", you are implying Jim deserves strong condemnation for some reason.
If you said, "Jim is a deplorable", that means something very different.
Last year, Hillary Clinton was running for president and said, "To just be grossly generalistic, you could put half of [her opponent Donald] Trump's supporters into what I call the basket of deplorables. Right? The racist, sexist, homophobic, xenophobic, Islamaphobic -- you name it." (Whatever else you say about her remark, she managed to promote six adjectives to nouns.)
In reaction, many Trump supporters tagged themselves "deplorables"; saying "Jim is a deplorable" means specifically he is a Trump supporter.
"Mandatory" has no such widespread use as a noun, but it's easy to see how it could happen in a community. Perhaps in your academic department, some courses are optional and others are mandatory, and this distinction is widely understood; the phrase "a mandatory" might come to mean "a mandatory course" -- just as in the workplace a temporary worker is "a temp", or in a haberdashery a large-size suit (or a large-size customer) is "a large".
Within the context of your department, you might easily say, "Occ Civ [Occidental Civilization] is a mandatory"; out that context, the sentence would be unintelligible.
In both the cases, mandatory is an adjective. What you're missing is the context.
is a mandatory
Structure #1 is obvious.
For conferencing to happen, internet connection is mandatory.
Structure #2 doesn't stand alone. Mandatory is describing a noun and whatever it is describing must follow.
For conferencing to happen, internet connection is a mandatory condition.
Mandatory can be used as a noun, as can virtually any other adjective. For example, Russian communists used to be called "Reds" after the color they identified their movement with. High-beam headlights for a long time were called "brights"—an adjective serving as a noun. There are countless other examples in English.
The primary use of the word mandatory is as an adjective, but it could be used as a noun under the right circumstances. For example,
There are certain mandatories that must be followed to do this job correctly: be attentive, be prompt, be courteous.
Compare this with the adjectival phrase "nice to have," which is turned into a noun with increasing frequency:
That is not a mandatory condition, but we all feel it is a "nice-to-have."
This is how people talk in the real world of English, whatever anyone else may tell you. Also note that the plural form, mandatories, is listed by some dictionaries as a noun all by itself, referring to people who have been given a mandate, or who are mandataries.