1. Consider the operations NoLeadingOrLaggingAs over languages that include the letter 'a' in their alphabet and Third, where

NoLeadingOrLaggingAs(L) = { x | w is in L and w = a*xa* where x neither starts nor ends in an 'a' }

MidThird(L) = { y | there exists a x and z, |x| = |y| = |z| and xyz is in L }

a.) & b.) Show Regular Languages are closed under each of these operations.

MidThird is challenging but can be shown using an NFA that is based on a DFA for L