In a certain 2-inputs logic gate, when inputs $\mathrm{A}=0$ and $\mathrm{B}=0$, then output $C=1$. And also when inputs $A=0, B=1$, then again output $C=1$. The gate must be

Analyzing the logic gate behavior:

Given input-output conditions:
• $A=0$, $B=0$ produces $C=1$
• $A=0$, $B=1$ produces $C=1$

The OR gate gives $C=A+B$:
For $A=0$, $B=0$: $C=0+0=0 eq1$
This violates the first condition.

The AND gate gives $C=A\cdot B$:
For $A=0$, $B=0$: $C=0\cdot0=0 eq1$
This violates the first condition.

The NAND gate gives $C=\overline{A\cdot B}$:
For $A=0$, $B=0$: $C=\overline{0\cdot0}=\overline{0}=1$
For $A=0$, $B=1$: $C=\overline{0\cdot1}=\overline{0}=1$
Both conditions are satisfied.

The NOR gate gives $C=\overline{A+B}$:
For $A=0$, $B=0$: $C=\overline{0+0}=\overline{0}=1$
For $A=0$, $B=1$: $C=\overline{0+1}=\overline{1}=0 eq1$
This violates the second condition.

Only the NAND gate satisfies both given input-output conditions.