$.$

As discussed in class, for certain functions which cannot be simplified beyond the sum of minterms,

i$.$e$.,$ for such functions, the sum of minterms representation has the same number of literals as any other

sum of products representation of this function.

a: Check if this condition is satisfied for the following functions:

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

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

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

b: Give an example of a Boolean function of three variables that satisfies this condition $($must be

different from any of the functions in $2($a$)).$

c: Describe in words how this condition can be verified if the function is given by a k$-$map