Peter Linz Edition 4 Exercise 4.1 Question 25 (Page No. 111)

Question

The $min$ of a language $L$ is defined as

          $min(L)=$ {$w∈L:$ there is no $u∈L,v∈Σ^+,$ such that $w=uv$}

Show that the family of regular languages is closed under the $ min$ operation.