turing machines

Question

consider a language which contains encodings of all DFA’s together with strings that the DFA’s accept.
L_DFA={ 〈B,w〉 | B is a DFA that accepts input string w}
Assume L_DFA ≤_m L_x, i.e. Problem L_DFA is polynomial time reducible to problem L_x.
 

1.    L_x must be regular
2.    L_x must be undecidable
3.    L_x must be decidable

Comments

 DFA’s together with strings that the DFA’s accept

@Nitish,@Ashwin,@Anu sir.
Encoding given accept string but does it reject other string which are not in language ! We can`t decide this property.? 

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@Saxena

what will be the outsider strings?.. DFA along with the strings which it doesn't accept.

in this case also DFA can reject strings in finite time

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What does " Assume L_DFA ≤_m L_x  mean?