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(b) Given languages A and B over alphabet , the interleaving of A and B is defined as {w | w = a1b1 . .

(b) Given languages A and B over alphabet , the interleaving of A and B is defined as {w | w = a1b1 . . . akbk, where a1 . . . ak A and b1 . . . bk B, each ai , bi }. Prove that the class of regular languages is closed under interleaving. Be careful: each ai , bi is a (possibly empty) string of symbols.

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