Assume that $(S,+,*)$ is a Boolean algebra. For all ainS, prove that $a=a*a$ using the laws

and properties of Boolean algebras.

Assume that $(S,+,*)$ is a Boolean algebra. For all ainS, prove that $a+1=1$ using the laws

and properties of Boolean algebras.

Assume that $(S,+,*)$ is a Boolean algebra. For all ainS, prove that $(a+b)*a=$a using the

laws and properties of Boolean algebras.

Write the Boolean expression that represents the combinatorial circuit in Figure $1$ and write

the output of each gate symbolically.

Find the complete sum$-$of$-$products expansion of the Boolean function $f$ of degree $3$ defined

by

$f(x,y,z)=(x+y)z.$