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~ on the US keyboard is in the same location as ¬ on the UK keyboard, and ~ is in ASCII. I have seen both in math books, but ~ is even used in some books which were printed before computers.

Hmm, according to the wikipedia article on ~, it's the original negation symbol in logic, and "Modern use has been replacing the tilde with the negation symbol (¬) for this purpose, to avoid confusion with equivalence relations."

I wonder when that started.

The LSAT only has English, no logical symbols are used. The the English in the test often has logical meaning. So when discussing that online, by convention students often use ~

If strikethrough is available, students use that instead quite often.

Maybe because there's a key for it on almost all keyboards?

I don't see why the LSAT would care when the SAT, GRE, etc. don't...