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Consider a Boolean gate $\text{(D)}$ where the output $Y$ is related to the inputs $A$ and $B$ as, $Y = A + \overline{B},$ where $+$ denotes logical $\text{OR}$ operation. The Boolean inputs $’0’$ and $’1’$ are also available separately. Using instances of only $\text{D}$ gates and inputs $’0’$ and $’1’,$ _______________ (select the correct option(s)).

1. $\text{NAND}$ logic can be implemented
2. $\text{OR}$ logic cannot be implemented
3. $\text{NOR}$ logic can be implemented
4. $\text{AND}$ logic cannot be implemented