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Question

is it a regular language? why?

Comments

isn’t it is the  set of all even length string ? which is if true  obviously regular .

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yes it is regular,

but why is it regular?

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every string in sigma* can be divided into two parts such that number of a’s in first part is same as number of b’s in second part. the regular expression is (a+b)*. if we can write regular expression for any language then it is regular.

take two length string for example  ‘aa’ i can write it as x=null string and y=aa, number of a in x is 0 and number of b in y is 0 so it is part of language.

take ‘bab, i can write it as x= ba and y=b, you can see it satisfies the condition

you can try to divide any length string , in such a way by yourself and verify.