3. Procrustean closure properties. Let be an alphabet, and let L3= theory, of, computing be an example language. (a) For any w=w1w2wn1wn, define STRETCH(w1w2wn)=w1w1w2w2wn1wn1wnwn. This induces an operation on languages, STRETCH(L)={STRETCH(w)wL}. For example, STRETCH(L3)={tthheeoorryy,ooff,ccoommppuuttiinngg}. Prove that if L is a regular language, then STRETCH(L) is also regular. (b) For any w=w1w2wn1wn with n2, define CHOP(w1w2wn1wn)=w2wn1. This induces an operation on languages, CHOP={CHOP(w)wLandw2}. For example, CHOP(L3)={heor,,omputin}. Prove that if L is a regular language, then CHOP(L) is also regular