Dont need to solve the complete pblm as it takes more time ...
1) current state value 0 on seeing input 00(values of (x,y)) should remain as 0 ... For this in JK-FF, I can give J=0,K=0 or J=0,K=1 ...
Now J = (x EXOR y)c = (x EXNOR y) will make J = 1 ... which is wrong because J has to be given input as 0 ... So A) and B) are eliminated ...
2) similiarly current state value = 1 on seeing input 10 (values of (x,y)) should be modified as 0 .. For this I need to give J = 0,K=1 or J = 1,K=1
Now Now K = (x EXOR y)c = (x EXNOR y) will make K = 0 ... which is wrong because k should be given value 1 ... So C) is eliminated ...
Option D) is the answer ...