Prove or disprove whether the following is a regular language

Question

I'm given the regular language L, and w being an element of L. If we remove the w from the language L, will the resulting language be still regular?

Well I thought to be true. Since initially is a regular language i.e. there exist an regular expression for it. And if we'd remove one string there would still exist a regular expression. Is it true?

Answer 1

Yes, $L$ is regular and the language $W=\{w\}$ is regular (finite languages are always regular). By closure properties of regular languages, $L-W$ is regular.