Question $3.$

$3\mathrm{.}1($a$)$ Convert the given Boolean expression to standard SOP $($Sum of Products$)$ form.

$x(ABC)=\frac{A}{b}ar(B)C\frac{+}{b}ar\frac{A}{b}ar(C)+$ABCD$+BCD$

$($b$)$ Write the Boolean expression for the following Logic circuit:

$3\mathrm{.}2($a$)$ Discuss the Positive edge triggered J$-$K flip flop and also provide its logic circuit.

$($b$)$ Draw the truth table of the Positive edge triggered J$-$K flip flop.

$3\mathrm{.}3$ Answer the following two questions:

$($a$)$ Apply Demorgan's theorems to the expression: $x\frac{?}{b}=ar((\frac{?}{\text{b}\text{a}\text{r}}(A)+B)(\frac{?}{\text{b}\text{a}\text{r}}(AC)))$