give example of 2 languages A and B such that A and B are undecidable but there concatenation A.B is decidable.
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closed as too localized by Andreas Blass, Andres Caicedo, Mark Sapir, Henry Cohn, Benjamin Steinberg Apr 30 '12 at 2:33
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Let $A$ contain all evenlength strings, plus an undecidable collection of oddlength strings. Let $B$ contain all oddlength strings, plus the empty string, plus an undecidable collection of evenlength strings. So each is undecidable, but the concatenation $AB$ consists of all strings and hence is decidable. 

