Explanation
Solving
Let A be the set of bit strings starting with 0.
Let B be the set of bit strings ending with 11.
We need to find the union: n(A∪B)=n(A)+n(B)−n(A∩B)
1. Calculate n(A) (Starts with 0):
The first bit is fixed as 0. The remaining 7 bits can be either 0 or 1.
2. Calculate n(B) (Ends with 11):
The last two bits are fixed as 11. The remaining 6 bits can be either 0 or 1.
3. Calculate n(A∩B) (Starts with 0 AND ends with 11):
The first bit is fixed (0) and the last two bits are fixed (11). This leaves 8−1−2=5 bits free.
4. Final Calculation:
Correct Option: 4. 160
