Since the specific logic circuit diagram is missing from the question, we deduce the intended output based on the provided probable answer. The Boolean expression $X = A \cdot B$ corresponds to an AND gate. In the context of standard AIPMT 2013 questions, this output is typically produced by a combination of universal gates, such as passing inputs A and B through a NAND gate followed by a NOT gate, or passing inverted inputs ($\overline{A}$ and $\overline{B}$) through a NOR gate.