Answer to Question #38620 in Math for Sujata Roy

Question

Nobody knows if P=NP at present. Consider a language L as defined below
L=(0+1)* if satisfiability is in P
L=(0*1)0* if satisfiability is not in P
L=(1*0)1* if 3-sat is in P
L=(0*1*)* if 3-sat is not in P
L=(0*1*0*1*)* if 0/1 knapsack problem is in P
L=(1*0*1*0*)* if 0/1 knapsack problem is not in P
L=(0*(00)*(1*11*)*) * if max-clique problem is in P
L=(0*(00)*(1*11*)*) * if node-cover problem is not in P
L=(0*1*)****(010)* if edge-cover problem is not in P
L=(0* + 1* + (00)* + (11)*)*(0100101010)* if the chromatic problem is not in P
What can we say about the string 0000111100001111=x
a) x is always in L
b) whether x is in L or not will be known after we resolve P=NP
c) the definition of L is contradictory
d) x can never be in L