A new flip flop with inputs X and Y, has the following property. Which of the…

To find the correct expression for the next state, we analyze the given truth table row by row to see which Boolean formula fits all cases.

From the table:
1. When X=0, Y=0: Next State is 1.
2. When X=0, Y=1: Next State is Q'.
3. When X=1, Y=1: Next State is 0.
4. When X=1, Y=0: Next State is Q.

Let's test the expression X'Q' + Y'Q:
- Case X=0, Y=0: (1)Q' + (1)Q = Q' + Q = 1. Matches row 1.
- Case X=0, Y=1: (1)Q' + (0)Q = Q'. Matches row 2.
- Case X=1, Y=1: (0)Q' + (0)Q = 0. Matches row 3.
- Case X=1, Y=0: (0)Q' + (1)Q = Q. Matches row 4.

Since the expression X'Q' + Y'Q correctly predicts the next state for all input combinations, it is the correct answer.