Use algebraic manipulation to change the equations above to get

equations for $1$ and $2$ use only NANDs and negation $($inverter$).$

~ The expression for $1$ must use three NANDs and two negations

$($inverters$).$

~ The expression for $2$ must use one NAND and two negations $($inverters$).$

Use truth tables to demonstrate that the two Boolean expressions for $1$ and

$2$ respectively are logically equivalent.

Hint: Use $=($

$$

$)+($

$$

$)$ and DeMorgan$$s Theorem.