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Another shibboleth to do with missing words is missing prepositions in US English: I've mainly seen this in cnn.com headlines, but people do it in speech too: "Let's do this Tuesday" rather than "Let's do this on Tuesday".

How would you say "Let's do that this afternoon."? I can't think of any other way to say it that isn't terribly awkward, and surely both "this afternoon" and "Tuesday" are noun-phrases.
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Bitt Faulk