Y by Adventure10, Mango247, and 1 other user
The Ababi alphabet consists of letters A and B, and the words in the Ababi language are precisely those that can be formed by the following two rules:
1) A is a word.
2) If s is a word, then
and
are words, where
denotes a word that is obtained by replacing all letters A in s with letters B, and vice versa; and
denotes the concatenation of x and y.
The Ululu alphabet consists also of letters A and B and the words in the Ululu language are precisely those that can be formed by the following two rules:
1) A is a word.
2) If s is a word,
and
are words, where
is defined as above and
is a word obtained from words x and y of equal length by writing the letters of x and y alternatingly, starting from the first letter of x.
Prove that the two languages consist of the same words.
1) A is a word.
2) If s is a word, then




The Ululu alphabet consists also of letters A and B and the words in the Ululu language are precisely those that can be formed by the following two rules:
1) A is a word.
2) If s is a word,




Prove that the two languages consist of the same words.