From the diagram
f=f1f2+f3 (put value)
=(4,5,6,7,8)f2+(1,6,15)=(1,6,8,15)Now, as you know that the number 0,1,2,... 14,15 represent the minterms like
Σm(6,8)(i) If you AND (4, 6) with (4, 5, 6, 7, 8) it will result in (4, 6) but we don't need 4, so option (a) is wrong.
(ii) If you AND (4, 8) with (4, 5, 6, 7, 8) it will result in (4,8) but we don't need 4, so option (b) is wrong.
(iii) If you AND (4, 6, 8) with (4, 5, 6, 7, 8) it will result in (4, 6, 8) but we don't need 4 here too, so option (d)is wrong.
(iv) If you AND (6, 8) with (4, 5, 6, 7, 8) it will result in (6,8) now when OR (6, 8) with (1,6, 15), you get (1,6, 8,15) which is f , so option (c) is correct