2. It is probably not surprising that any truth table on n variables can be expressed with some (perhaps complicated) formula using only the logical connectives AND, OR, and NoT. owever, t might be a little surprising to learn that certain binary operations are universal meaning that it is possible to generate any truth table using only that binary operation! The binary operation NAND is one such example P QTQ TTIF TFT F TT FFT In this question we will figure out how to replace AND, OR, and Nor with equivalent operations built from NANDs. For each of the following parts use only P, Q, parentheses, and the NAND operation defined above (a) Write down the truth table for PP. What operation is this? b) Write down a logical formula for AND and prove that your formula is equivalent. c Same question as part (b), except for OR