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To get tautology output of $F$ should be $1$.

option 1) $F=(x+y)+ \overline{xy}$

applying de-morgon’s law:

$F=x+y+ \bar x+\bar y$

$F=(x+\bar x)+(y+\bar y)$

$F=1 (\because x+\bar x=1) $

So option $A$ ,$\text{NAND gate}$ is correct.

we can check remaining options but none of them give $1$ as output.

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