Is the use of “men” or “man” as a term or representative for “mankind” synecdoche?

No. That would really be a synonym.

A “synecdoche” is a completely different phrase that is understood to represent the intended subject. In this case, “men” and “mankind” might be synecdoches for “humanity” – inclusive of all men, women, children, boys and girls – instead of the specific adult male gender.

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