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Recently, I had to use the following sentence:

"The paths of the php and html files are as follows..."

It's about one html file and one php file. Both have one path and they are separate files.

When I refer to "the paths" of these two different files, does it need to be plural, or singular since it's one path for two distinct entities?

What about "files"? Does that need to be plural? Or should it be singular, since it's one html file and one php file?

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You are using the word "paths". This requires the verb "are" to agree. If you were to refer to the "php or html file" that would be telling the reader that they are two different terms for the same or equivalent thing. Then a singular "path - is" would work.

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Both need to be plural. There are, after all, two files and two paths in your original sentence. The ambiguity is arising from the method of construction, consider the following rearrangement instead:

The php and html filepaths are as follows...

In this construction, file and path are concatenated into a single noun. It's apparent then that the noun represents more than one of each, hence plural. It follows that individual components from the noun are also plural.

Also, see the following Q&A for the etymology of filepath versus file path versus file-path: Discussion of filepath on StackExchange

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