7. [10 bonus points] 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):wL} 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 , then truncate (L) is also regular