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Sometimes 'Tis will be used to represent "this is" and 'em will be used as "them" in spoken English, but how do I typeset them with TeX? Should the tick mark be "left quote" or "right quote" or some other symbol?

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I think that 'tis usually means "it is", but no matter. Typeset them as you did here, with apostrophes (single right quotes).

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Sounds right to me. Apostrophes can be used to represent elided letters, as in mustn’t and other contractions. This is the same thing with nothing on the left-hand side of the contraction. – Matthew Leingang May 2 '11 at 2:49

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