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1. Determine the regular expression for all strings containing exactly one ‘a’ over ∑ = {a, b, c}.

Solution:

We have the input alphabets are ∑ = {a, b, c}

The objective of the problem is to find out the regular expression for all strings containing exactly one ‘a’.

For this, first find out the regular expression for any strings at all over the given ∑, which does not contain any ‘a’. It is-

(b + c)*

Thus, to write a regular expression which denote all string containing exactly on ‘a’ we simply put the regular expression for any string at all which does not contain any ‘a’ on the both side of ‘a’. Thus, the resultant regular expression is-

(b + c)* a (b + c)*

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