You're wrong. Just read the examples from "ΜετάEd" and my own. Everyone is a synonym of everybody, all and the whole, but that doesn't mean every one of them being the same.
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Everybody does this problem perfectly fine during the test. "Do" is usually used to form imperative sentences or commands, in this case do this problem, which is perfectly fine. does this problem also works, but note the difference in context.
The 'if you’re in Britain, you don’t have to worry so much about everyone and everybody because sometimes they’re considered plural' is absolutely wrong. 'Everyone needs to take their own lunch' is acceptable because it uses singular their.
Also, everybody is used more often than everyone in spoken language, which makes sense if it's more informal. Having said this, it's absolutely fine to use either one.
word choice - "Everyone" or "everybody" - English Language & Usage ...
Welcome, everybody! Which is equivalent to, for example: Welcome, Janet! Without the comma as a sentence, it would be, for example: Janet, go and welcome everybody so they understand the party has already started. As whether everybody and everyone are interchangeable - yes, they are. It doesn't matter which one you use in this case.
Are "everyone", "everybody", "everything", and "everywhere" singular or plural. I have found people who are say they are singular but also people who say they are plural.