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Universities and Xiao Xu.
Xiao Zhang is older than an engineer, which means that Xiao Zhang is not an engineer, and Xiao Li is different from a mathematician, which means that Xiao Li is not a mathematician and a mathematician is younger than Xiao Xu, which means that Xiao Xu is not a mathematician, while Xiao Li and Xiao Xu are not mathematicians, so only Xiao Zhang is a mathematician. However, it can be seen from the two sentences that Xiao Zhang is older than an engineer and younger than Xiao Xu that Xiao Xu is not an engineer, so only Xiao Xu is a teacher and Xiao Li is an engineer.

Therefore, Xiao Xu is a teacher, Xiao Zhang is a mathematician and Xiao Li is an engineer.

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