Then you should know about the JK Flip Flop Characteristic table
Characteristic Table
J |
K |
Qn |
Qn+1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
Excitation Table of JK we make with help of Characteristic Table
Qn |
Qn+1 |
J |
K |
0 |
0 |
0 |
# |
0 |
1 |
1 |
# |
1 |
0 |
# |
1 |
1 |
1 |
# |
0 |
As function Table mentioned in the question above with the help of that we fill Qn+1. And with the help of Excitation table of JK we will JK values
A |
B |
Qn |
Qn+1 |
J |
K |
0 |
0 |
0 |
1 |
1 |
# |
0 |
0 |
1 |
0 |
# |
1 |
0 |
1 |
0 |
1 |
1 |
# |
0 |
1 |
1 |
1 |
# |
0 |
1 |
0 |
0 |
0 |
0 |
# |
1 |
0 |
1 |
1 |
# |
0 |
1 |
1 |
0 |
0 |
0 |
# |
1 |
1 |
1 |
0 |
# |
1 |
Minterm of J in form of AB = A'B'+A'B
Minterm of K in form of AB = A'B'+AB
D option Match this way.