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Suppose there are three languages (i.e.. problems), of which we know the following: 1. LI ism P. 2. L2 is NP-complete. 3. L3 is not

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Suppose there are three languages (i.e.. problems), of which we know the following: 1. LI ism P. 2. L2 is NP-complete. 3. L3 is not in NP. Suppose also that we do not know anything about the resolution of the "P vs. NP" question; for example, we do not know definitely whether P=NP. Classify each of the following languages as (a) Definitely in P. (b) Definitely in NP (but perhaps not in P and perhaps not NP-complete) (c) Definitely NP-complete (d) Definitely not in NP: L1 [union] L2. L1 intersection L2. L2cL3. where c is a symbol not in the alphabet of L2 or L3 (i.e.. the marked concatenation of L2 and L3. where there is a unique marker symbol between the strings from L2 and L3). The complement of L3. Based on your analysis, pick the correct, definitely true statement from the list below. a) L1 [union] L2 is definitely not in NP. b) L2cL3 is definitely not in NP. c) L1 intersection L2 is definitely not in NP. d) The complement of L3 is definitely not in NP

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