In this problem we'll explore the fact that all logical circuits can be implemented using just NAND gates. The figure below shows you the symbol for a NAND gate and its truth table. We then show you how NAND gates can be wired together to perform the equivalent of a NOT gate,an AND gate, and an OR gate.

i. Let's denote p NAND q as paq. Write a logical expression for the three circuits correspondingto AND, OR, and NOT. ii. Validate your three logical expressions with three truth tables. For clarity and full credit,show each variable and distinct sub-clause in a separate column, culminating in your final formula.