Shine Bright Like a Diamond $[20$ points$]$

Consider a new logical operator diamond $(\frac{\frac{?}{?}}{?}$ diamond in latex$).$ For this problem, we define adiamondb by the following truth

table:

Even though this is a new operator, we can still use it to create circuits representing other operators we have seen

before! Here is an example drawing of the diamond gate:

$($a$)$ Using only diamond gates and the input $a,$ create a circuit whose output represents nota. You may use multiple copies

of $a$ as inputs if required.

$($b$)$ Using only diamond gates and the inputs a and $b,$ create a circuit that's output represents $a^{{?}^{?}}b.$ You may use multiple

copies of $a,b$ as inputs if required.