$1.(4$ points$)$ Which gates are called "universal" gates? Why?

$2.(6$ points$)$ Draw logic circuits AND, OR$,$ and NOT using universal gate NAND.

$3.(6$ points$)$Draw logic circuits AND, OR$,$ and NOT using universal gate NOR.

$4.(24$ points$)$ Draw the logic diagram corresponding to the following Boolean expressions.

$[$Do not simplify these functions$]$

a$.$ B$$ C$+$ AB $+$ ACD$$

b$.($A $+$ B$)($C $+$ D$)($A $+$ B $+$ D$)$

c$.($A$$ B $+$ A$$B$)($CD$+$ CD$)$

d$.$ A$+$ CD $+($A $+$ D$)($C $+$ D$)$

$5.(10$ points$)$ Draw a logic diagram of the circuit that implement the following function

using AND, OR$,$ and NOT gates. $[$Do not simplify this function.$]$

F $=[[$A $($B $+$ C$)+$ B$$DE$]($A$+$CE$)]$

Solve.