1. (6 points)                      

!(!A*!B+B)

  DeMorgan  Hint :  !((!A*!B)+B) 

!(!A*!B) * !B 

  DeMorgan.

(!!A+!!B) * !B

  Cancellation

(A+B)*!B

  Distribution

A*!B + B*!B

   Inverse or Complement

A*!B + 0

   Identity

A*!B

2. (7 points)                        
!(A*!B+B)

  DeMorgan

!(A*!B)*!B

  DeMorgan

(!A+!!B)*!B

  Cancellation

(!A+B)*!B

  Distribution

!A*!B+B*!B

  Inverse

!A*!B+0

  Identity

!A*!B

  DeMorgan

!(A+B)

3. (8 points)                        
(A+B)*(A+C)*(!B+!C)

   Distribution

(A+B*C)*(!B+!C)

   Distribution

(A*!B)+(B*!B*C)+(A*!C)+(B*C*!C)

   Inverse

(A*!B)+(0*C)+(A*!C)+(B*0)

   Null

(A*!B)+(0)+(A*!C)+(0)

   Identity

(A*!B)+(A*!C)  

   Distribution

A(!B+!C)

   DeMorgan

A*!(B*C)