Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

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.

--------------------------------------------------------------------------

(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.

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.