$(8$ Pts$)$ For the following Truth Table, se a K$-$Map to derive a minimum Boolean expression for the

output. Draw the logic circuit. Label the output of each gate and the final output with a Boolean

Expression

$(9$ Pts $-3$ Pts Each$)$ Apply DeMorgan's Theorem for NAND gates and use only $2-$Input NAND Gates to

a$.$ Create and sketch a simplified circuit with AND gate functionality.

b$.$ Prove the function of your design using DeMorgan's and$/$or other Boolean Theorems.

c$.$ Prove the function of your design using Truth Tables

$(9$ Pts $-3$ Pts Each$)$ Apply DeMorgan's Theorem for NAND gates and use only $2-$Input NAND Gates to

a$.$ Create and sketch a simplified circuit with OR gate functionality.

b$.$ Prove the function of your design using DeMorgan's and$/$or other Boolean Theorems

c$.$ Prove the function of your design using Truth Tables