Regular Expression

Question

Hi Mates,

Is it true or false..?

The regular expression for the language L={vuv|v,u∈{a,b}*,|v|≤3 } is L=(a+b)*..?

Please answere with explanation.

Thanks

Comments

L={VUV | V,U $\epsilon (a,b)^{*}$ }

consider V=$\epsilon$ and U=$(a+b)^{*}$  then it is complete language.

So L=$(a+b)^{*}$.

Answer 1

For any string x∈{a,b}*, we can treat it as x=ϵxϵ, where v=ϵ,x=u. Therefore, any string x∈{a,b}* is in L. Thus, L = (a + b)*