Q.How many two input NAND gates must be used to produce two input OR function?

A universal gate is a logic gate from which every other gate and, therefore, any digital circuit can be constructed. The NAND gate and the NOR gate are the two universal gates.

The NAND gate is an AND gate followed by an inverter, so $Y = \overline{A \cdot B}$; the NOR gate is an OR gate followed by an inverter, so $Y = \overline{A + B}$. Their power comes from the fact that inversion is built in. Using only NAND gates: a single NAND with its inputs tied together gives NOT; two NANDs give AND; three NANDs give OR; and four NANDs give an XOR. Similarly, using only NOR gates one NOR gives NOT, two give OR, three give AND, and four give an XNOR. To produce a two-input OR function you need three NAND gates, and to produce it with NOR gates you need two NOR gates. …