BdMO National Junior 2009/10

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samiul_samin
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BdMO National Junior 2009/10

Unread post by samiul_samin » Sun Feb 24, 2019 12:27 pm

In a strange language there are only two letters,a and b,and it is postulated that the letter a is a word.Furthermore all additional words are formed according to the following rules:
$(i)$ Given any word ,a new word can be formed from it by adding one b at the right hand end.
$(ii)$ If in any word a sequence aaa appears ,a new word can be formed by replacing aaa by the letter b.
$(iii)$ If in any word a sequence bbb appears ,a new word can be formed by omitting bbb.
$(iv)$ Given any word,a new word can be formed by writing down the sequence that constitutes the given word twice.
For example $(iv)$, aa is a word and by $(iv)$ again aaaa is a word,Hence by $(ii)$ ba is a word,and by $(i)$, bab is also a word.Again by $(i)$ babb is a word,and so by $(iv)$ babbbabb is also a word.Finally ,by $(iii)$ we fond that baabb is a word.
Prove that in this language baabaabaa is not a word.

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