Let us define an operation $truncate$, which removes the rightmost symbol from any string. For example, $truncate (aaaba)$ is $aaab$. The operation can be extended to languages by
$truncate (L)= $ {$truncate(w):w ∈ L$}
Show how, given a dfa for any regular language L, one can construct a dfa for $truncate (L)$.
From this, prove that if $L$ is a regular language not containing $λ$, then $truncate (L)$ is also regular.
