Answer Happy

Theory of Computation.
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1. This problem is based on problem 7.6 in Sipser. We will prove that P is closed under complement, union, intersection, and concatenation. Formally, let L1, L2 be formal languages with L1, L2 E P - that is, both languages can be recognized in polynomial time (a) (5 points) Prove that L1 = {w\w & Li} E P (b) (5 points) Prove that Lį U L2 = {W/W E Lį or w E L2} E P (c) (5 points) Prove that Li oL2 = {w/w = xy for some x e L1, y € L2} € P = = = =