Logic Gates question from JEE Main 2024 (9 Apr, Shift 2)

Answer: (a)

1. Upper AND: $AB$. Lower AND gets $\bar{A}$ and $\bar{B}$: $\bar{A}\bar{B}$.
2. $E = \overline{AB + \bar{A}\bar{B}}$ (NOR).
3. $A = 0, B = 1$: $AB = 0$, $\bar{A}\bar{B} = 0 \Rightarrow X = 1$.
4. $A = 1, B = 0$: also both terms $0 \Rightarrow Y = 1$.
5. So the answer is (a) 1, 1.