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Que. Consider two languages L1 and L2 each on the alphabet ∑. Let f : ∑ → ∑ be a polynomial time computable bijection such that (∀ x) [x ∈ L1 iff f(x) ∈ L2]. Further, let f^-1 be also polynomial time computable. Which of the following CANNOT be true?
a. L1 ∈ P and L2 is finite
b. L1 ∈ NP and L2 ∈ P
c. L1 is undecidable and L2 is decidable
d. L1 is recursively enumerable and L2 is recursive
Answer:L1 is undecidable and L2 is decidable
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