please solve all of them $($#$27,$ #$28,$ #$29)$

Practice Exercise $2\mathrm{.}7$

Find a product of maxterms expression for $F(x,y,z)=(1,2,3,5,7).$

Answer: $F^{\text{'}}=(0,4,6)$ and $F=(x+y+z)(x^{\text{'}}+y+z)(x^{\text{'}}+y^{\text{'}}+z)$

Practice Exercise $2\mathrm{.}8$

Find a sum of minterms expression for $F=(1,3,4,6).$

Answer: $F(x,y,z)=(0,2,5,7)=x^{\text{'}}{y}^{\text{'}}{z}^{\text{'}}+x^{\text{'}}y{z}^{\text{'}}+x{y}^{\text{'}}z+xyz$

Practice Exercise $2\mathrm{.}9$

Identify the minterms and maxterms of the truth table for $F$ shown below.

Answer: $F=(1,3,4,6)=(0,2,5,7)$

Standard Forms

The two canonical forms of Boolean algebra are basic forms that one obtains from read$-$

ing a given function from the truth table. These forms are very seldom the ones with the

least number of literals, because each minterm or maxterm must contain, by definition,

all the variables, either complemented or uncomplemented.

Another way to express Boolean functions is in standard form. In this configuration

the terms that form the function may contain one, two, or any number of literals. There

are two types of standard forms: the sum of products and products of sums.

The sum of products is a Boolean expression containing AND terms, called prodwo

terms, with one or more literals each. The sum denotes the ORing of these terms As

example of a function expressed as a sum of products is

$F_1=y^{\text{'}}+xy+x^{\text{'}}y{z}^{\text{'}}$

The expression has three product terms, with one, two, and three literals. Their sum is

in effect, an OR operation.