GATE | GATE-CS-2004 | Question 89

L1 is a recursively enumerable language over Σ. An algorithm A effectively enumerates its words as w1, w2, w3, … Define another language L2 over Σ Union {#} as {wi # wj : wi, wj ∈ L1, i < j}. Here # is a new symbol. Consider the following assertions.

S1 :  L1 is recursive implies L2 is recursive
S2 : L2 is recursive implies L1 is recursive 

Which of the following statements is true ?
(A) Both S1 and S2 are true
(B) S1 is true but S2 is not necessarily true
(C) S2 is true but S1 is not necessarily true
(D) Neither is necessarily true

Answer: (A)


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