1. (i) Words having 1 letter : b Words having 2 letters : bb, ab, ba Words havin
ID: 3629021 • Letter: 1
Question
1.(i)
Words having 1 letter :
b
Words having 2 letters :
bb, ab, ba
Words having 3 letters :
bbb, bab, bba, abb
Words having 4 letters :
bbbb, bbab, bbba, abbb, abab, abba, babb, baab, baba
Words having 5 letters :
bbbbb, bbbab, bbbba, bbabb, babbb, abbbb, abbab, abbba, ababb, babab, bbaba, baabb, bbaab.
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(ii)
'baaab' is NOT a word in the above language.
It is because 'a' can be followed by maximum another 'a' and after that, 'b' comes.
So, there can be atmost 2 'a' together.
Also, in the part (i) of this question, we could list no such word.
Hence,
'baaab' is NOT a word in the above language.
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(iii)
Another way of describing the words in the language is :
S* = Words formed from 'a' and 'b' having at least one 'b' and atmost 2 'a' such that 2 'a's cannot occupy together the 1st-2nd and 2nd last and Last letters of the word.
Explanation / Answer
1. (i) Words having 1 letter : b Words having 2 letters : bb, ab, ba Words having 3 letters : bbb, bab, bba, abb Words having 4 letters : bbbb, bbab, bbba, abbb, abab, abba, babb, baab, baba Words having 5 letters : bbbbb, bbbab, bbbba, bbabb, babbb, abbbb, abbab, abbba, ababb, babab, bbaba, baabb, bbaab. -------------------------------------------------------------------------- (ii) 'baaab' is NOT a word in the above language. It is because 'a' can be followed by maximum another 'a' and after that, 'b' comes. So, there can be atmost 2 'a' together. Also, in the part (i) of this question, we could list no such word. Hence, 'baaab' is NOT a word in the above language. ------------------------------------------------------------------------- (iii) Another way of describing the words in the language is : S* = Words formed from 'a' and 'b' having at least one 'b' and atmost 2 'a' such that 2 'a's cannot occupy together the 1st-2nd and 2nd last and Last letters of the word.
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