Which one of the followings is equivalent to the Boolean expression $F(x,y,z)=(1,2,3,7)?$

D$.x^{\text{'}}(y+z)+yz$

A$.x^{\text{'}}y+x^{\text{'}}z+xz$

B$.xy+x^{\text{'}}z+xz$

C$.x^{\text{'}}y+xz+xz$

E$.$ None of them.

Following $2$ questions are related to the same Boolean expression.

$5.$ Which one of the followings is a prime implicant of the Boolean expression $F(w,x,y,z)=(1,3,4,5,6,7,8,9,11,14,15)?$

A$.yz$

B$.w{y}^{\text{'}}$

C$.x^{\text{'}}{y}^{\text{'}}$

D$.w{x}^{\text{'}}y$

E$.$ None of them.

$6.$ Which one of the followings is an essential prime implicant of the Boolean expression $F(w,x,y,z)=(1,3,4,5,6,7,8,9,11,14,15)?$

A$.wx$

B$.w^{\text{'}}x$

C$.wyz$

D$.w{x}^{\text{'}}{y}^{\text{'}}$

E$.$ None of them

Following $2$ questions are related to the same Boolean expression.

$7.$ Which one of the followings is equivalent to Boolean expression $F(w,x,y,z)=(1,3,4,5,6,7,8,9,11,14)?$

A$.$ All of them.

B$.w^{\text{'}}zz+w^{\text{'}}x+x^{\text{'}}z+xy{z}^{\text{'}}+w{x}^{\text{'}}{y}^{\text{'}}$

C$.w^{\text{'}}z+w^{\text{'}}z+w^{\text{'}}x+x^{\text{'}}z+xy{z}^{\text{'}}+w{x}^{\text{'}}{y}^{\text{'}}$

D$.w^{\text{'}}z+w^{\text{'}}x+x^{\text{'}}z+xy{z}^{\text{'}}+w{x}^{\text{'}}{y}^{\text{'}}$

E$.w^{\text{'}}z+w^{\text{'}}x+x^{\text{'}}z+xy{z}^{\text{'}}+w{x}^{\text{'}}{y}^{\text{'}}+w{x}^{\text{'}}{y}^{\text{'}}w$

$8.$ Which one of the followings is equivalent to Boolean expression $F(w,x,y,z)=(1,3,4,5,6,7,8,9,11,14)?$

A$.(w+x+z)(x+y^{\text{'}}+z)(w^{\text{'}}+x^{\text{'}}+y)(w^{\text{'}}+x^{\text{'}}+z^{\text{'}})$

B$.(w+x+z)(x+y^{\text{'}}+z^{\text{'}})(w^{\text{'}}+x+y)(w^{\text{'}}+x^{\text{'}}+z^{\text{'}})$

C$.(w+x+z)(x+y^{\text{'}}+z^{\text{'}})(w^{\text{'}}+x+y)(w+x^{\text{'}}+z^{\text{'}})$

D$.(w+x+z)(x+y^{\text{'}}+z^{\text{'}})(w^{\text{'}}+x^{\text{'}}+y)(w^{\text{'}}+x^{\text{'}}+z^{\text{'}})$

E$.$ None of them

$9.$ Which of the followings is equivalent to Boolean expression $A{B}^{\text{'}}C+A^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}D+A{B}^{\text{'}}D+A^{\text{'}}B{C}^{\text{'}}+$ABCD $?$ State the correct option.

A$.A^{\text{'}}BC+$ACD$+A^{\text{'}}{B}^{\text{'}}C+B^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}$

B$.A^{\text{'}}B{C}^{\text{'}}+$ACD$+A{B}^{\text{'}}C+B^{\text{'}}{C}^{\text{'}}D$

C$.A^{\text{'}}BC+$ACD$+A^{\text{'}}{B}^{\text{'}}C+B^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}$

D$.A^{\text{'}}BC+A{C}^{\text{'}}D+A{B}^{\text{'}}C+B^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}$

E$.A^{\text{'}}BC+A{C}^{\text{'}}D+A{B}^{\text{'}}C+B^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}$