Question

Give a regular expression for each of the following languages.

r. { x∈{a, b}* | the number of as in x is odd}∪{bn​ ​ | n is odd}∪{(aba)n​ ​}

s. {an​ ​| n is divisible by at least one of the numbers 2, 3, or 5}

q. {x∈{a, b}* | the number of as in x is odd}

u. {xy ∈ {a, b}* | the number of as in x is odd and the number of bs in y is even}

Answer 1

q:

b*ab*(b*ab*ab*)*

The part in () represent number of even a's. we add one a in front to make it odd.

r:

b*ab*(b*ab*ab*)* + b(bb)* + (aba)*

first part for odd a, second for odd bs and third for aba

s:

(aa)* + (aaa)* + (aaaaa)*

first for 2, second for 3 and third for 5

u:

(b*ab*(b*ab*ab*)*).((a*ba*ba*)*a*)

x = b*ab*(b*ab*ab*)*

y = (a*ba*ba*)*a*

Hope this helps.

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