Give a recursive de$$nition for the set of all strings of a$$s and b$$s where all the strings start and end with different symbols. $($Assume$,$ S is set of all strings of a$$s and b$$s where all the strings of all strings of a$$s and b$$s where all the strings start and end with different symbols.Then S $=\{$ab$,$ ba$,$ aab, abb, baa, bba, abab, aabb, baba, bbaa, $...\}).$