doubt

Question

Define init (L) = {set of all prefixes of L}
Let L = {w | w has equal number of 0’s and 1’s}, Ʃ = {0,1}
init (L) is:
(a) all binary strings with unequal number of 0’s and 1’s
(b) all binary strings with ԑ-string
(c) all binary strings with exactly 1 more 0’s than the number of 1’s
or one more than number of 0’s
(d) None of above

Answer 1

Let L = {epsilon, 01, 10, 0011, 0101, 0110, 1100, 1010, 1001....}

Init L = {epsilon, 0, 1, 00, 11, 01, 10, ... } = (0+1)*

So Option B