Logic Gates question from JEE Main 2013 (25 Apr, Shift 1)

Answer: (a)

1. From the table, $C = 1$ only for $A = 1, B = 0$: $C = A\bar{B}$.
2. (a): NOR of $\bar{A}$ and $AB$: $C = A\cdot\overline{AB} = A(\bar{A} + \bar{B}) = A\bar{B}$. Matches.
3. (b) gives $B(A + B) = B$; (d) gives $\overline{AB}$; neither matches.
4. So the answer is (a).