The resultant logic gate from the combination of following gates is

Circuit Analysis

The circuit consists of two NOT gates followed by a NOR gate with inputs $A$ and $B$.

The first NOT gate inverts input $A$, producing $A'$.

The second NOT gate inverts input $B$, producing $B'$.

These signals are fed into a NOR gate, yielding output $Y = (A' + B')'$.

Applying De Morgan's theorem, $(X + Y)' = X' \cdot Y'$, so $Y = (A')' \cdot (B')'$.

Since double inversion returns the original variable, $(A')' = A$ and $(B')' = B$, so $Y = A \cdot B$.

This is the Boolean expression for an AND gate.