give example of 2 languages A and B such that A and B are undecidable but there concatenation A.B is decidable.



example :concatenation of 2 undecidable language gives a decidable language
Let $A$ contain all even-length strings, plus an undecidable collection of odd-length strings. Let $B$ contain all odd-length strings, plus the empty string, plus an undecidable collection of even-length strings. So each is undecidable, but the concatenation $AB$ consists of all strings and hence is decidable.


