I'm told that given the alphabet
I have to find the regular expression for a language that has at most two
I came up with this answer
$b^*$ U $b^*a$ $b^*$ U $b^*a$ $b^*$ $a$ $b^*$
So for the case with no A's, we can have any number of b's, for the case with 1 a, we have any number of b's followed by an a, followed by any number of b's. For the third case, we have exactly two a's.
Is this correct? Would this be a good way of going about solving these? Is there a general strategy to doing regular expressions?
Because my textbook gave me a completely different answer of:
$b^*(Є U a)b^*(ЄUa)b^*$
Where Є is the empty string, U is union (+).
Any input would be much appreciated.