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The first gate is a standard two-input NAND gate. Its output is the inverse of the AND operation:
$$\text{Output}_1 = \overline{A \cdot B}$$
The second gate is a NAND gate with its inputs tied together. The output of the first gate is inverted by the second gate:
$$Y = \text{NOT}(\text{Output}_1) = \overline{\overline{A \cdot B}}$$
$$Y = A \cdot B$$
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