a$).$ List two types of universal logic gates.

b$).$ Construct or implement an XOR gate and XNOR gate using each of the universal gate listed above.

c$).$ Use the tabular method to simplify or solve the Boolean function below and use the chart to remove the redundant prime implicants:

F $($A$,$ B$,$ C$,$ D$)=\backslash$Sigma $(0,1,2,3,5,7,8,10,12,13,15).$

d$).$ A majority circuit is a combinational circuit whose output is equal to $1$ if the input variables have more $1$s than $0$s otherwise. Design a three$-$input majority circuit by finding the circuit$$s truth table, Boolean equation, a logic diagram and a K$-$MAP for the same.

e$).$ Given the following Boolean expression;

BC $+$ AD $=($A $+$ B$)($B $+$ D$)($A $+$ C$)($C $+$ D$).$

Prove that the RHS $=$ LHS $.$