Funny enough, I've only seen it at the Gymnasium (secondary level) and not in the University a few years later -- then indeed the usual symbols were the 'slashed' relations like you've described, or the bottom symbol: ⊥ in logic. Maybe it's an idiosyncrasy of a certain subset of math teachers.

But how would you position the slash to get a somewhat easy to decipher symbol? To me, the right angle symbol seems to lend itself more to this unorthodox negation through the contradiction symbol than to negation through the normal slash.