£* {0,1} = {€, 0,1 ,01 ,11 , 000, 001, 010, 100, 011,101,110,111,.............}
And language L containing sub- string 100 I.e L =(0+1)*100
If we subtract £* -L then we get only those string which not having substring as 100
£*-L = {€, 0, 1, 00, 11, 10,01, 000, 001, 010, 011, 101, 110, 111,............ }
Let's check options ,
A) false beacse It can not generate string 01 but it is present in £*-L hence option A fails
B) it produce sub-string 100 in 10100 string so it fails and it can not produce € so it fails
C) unable to produce € hence it fails
D) it produce all string over £*-L hence option D correct